JEE Main & Advanced Mathematics Straight Line Question Bank

done Slope of line, Equation of line in different forms Total Questions - 129

• question_answer1)
  Slope of a line which cuts intercepts of equal lengths on the axes is                                  [MP PET 1986]o00000
  A)
             - 1   done clear
  B)
             0 done clear
  C)
             2      done clear
  D)
             \[\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer2)
  If the coordinates of the points A and B be (3, 3) and (7, 6), then the length of the portion of the line AB intercepted between the axes is
  A)
             \[\frac{5}{4}\]                            done clear
  B)
             \[\frac{\sqrt{10}}{4}\] done clear
  C)
             \[\frac{\sqrt{13}}{3}\]               done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer3)
  If the line \[2x+3y=5\]and \[y=mx+c\]be parallel, then
  A)
  m = 2/3, c = 5                            done clear
  B)
  m = - 2/3, c = 5 done clear
  C)
  m = - 2/3, c = any real number done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer4)
  The line \[(3x-y+5)+\lambda (2x-3y-4)=0\]will be parallel to y-axis, if l =        
  A)
             \[\frac{1}{3}\]                            done clear
  B)
             \[\frac{-1}{3}\] done clear
  C)
             \[\frac{3}{2}\]                            done clear
  D)
             \[\frac{-3}{2}\] done clear
  View Solution play_arrow

• question_answer5)
  If the transversal y = mr x; r = 1, 2, 3 cut off equal intercepts on the transversal \[x+y=1,\]then \[1+{{m}_{1}},\]\[1+{{m}_{2}},\] \[1+{{m}_{3}}\] are in            
  A)
             A. P.                                            done clear
  B)
             G. P. done clear
  C)
             H. P.                                           done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer6)
  The gradient of the line joining the points on the curve \[y={{x}^{2}}+2x\]whose abscissa are 1 and 3, is  [MP PET 1997]
  A)
             6      done clear
  B)
             5 done clear
  C)
             4      done clear
  D)
             3 done clear
  View Solution play_arrow

• question_answer7)
  The parallelism condition for two straight lines one of which is specified by the equation \[ax+by+c=0\]the other being represented parametrically by \[x=\alpha \text{ }t+\beta ,\] \[y=\gamma \text{ }t+\delta \]  is given by                                                              [AMU 2000]
  A)
             \[\alpha \gamma -b\alpha =0\], \[\beta =\delta =c=0\]            done clear
  B)
             \[a\alpha -b\gamma =0\], \[\beta =\delta =0\] done clear
  C)
             \[a\alpha +b\gamma =0\]        done clear
  D)
             \[a\gamma =b\alpha =0\] done clear
  View Solution play_arrow

• question_answer8)
  The equation of the straight line which passes through the point (1, - 2) and cuts off equal intercepts from axes, is  [MNR 1978]
  A)
             \[x+y=1\]                                    done clear
  B)
             \[x-y=1\] done clear
  C)
                  \[x+y+1=0\]             done clear
  D)
                  \[x-y-2=0\] done clear
  View Solution play_arrow

• question_answer9)
  The equations of the lines which cuts off an intercept -1 from y-axis are equally inclined to the axes are
  A)
  \[x-y+1=0,\ \ x+y+1=0\]      done clear
  B)
  \[x-y-1=0,\ \ x+y-1=0\] done clear
  C)
  \[x-y-1=0,\ \ x+y+1=0\]        done clear
  D)
  None of these   done clear
  View Solution play_arrow

• question_answer10)
  A line L is perpendicular to the line \[5x-y=1\]and the area of the triangle formed by the line L and coordinate axes is 5. The equation of the line L is                                                            [IIT 1980; RPET 1997]
  A)
             \[x+5y=5\]                               done clear
  B)
             \[x+5y=\pm 5\sqrt{2}\] done clear
  C)
             \[x-5y=5\]                                 done clear
  D)
              \[x-5y=5\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer11)
  The equation of the line whose slope is 3 and which cuts off an intercept 3 from the positive x ? axis is
  A)
             \[y=3x-9\] done clear
  B)
             \[y=3x+3\] done clear
  C)
             \[y=3x+9\]                               done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer12)
  If the coordinates of the points A, B, C, D, be \[(a,\ b),\] \[({a}',\ {b}'),\] \[(-a,\ b)\] and \[({a}',\ -{b}')\] respectively, then the equation of the line bisecting the line segments AB and CD is
  A)
             \[2{a}'y-2bx=ab-{a}'{b}'\]     done clear
  B)
             \[2ay-2{b}'\ x=ab-{a}'{b}'\] done clear
  C)
             \[2ay-2{b}'x={a}'b-a{b}'\]     done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer13)
  The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is                  [MNR 1979]
  A)
             \[x-y=5\]                                   done clear
  B)
             \[x+y=5\] done clear
  C)
             \[x+y=1\]                                 done clear
  D)
             \[x-y=1\] done clear
  View Solution play_arrow

• question_answer14)
  If the coordinates of A and B be (1, 1) and (5, 7), then the equation of the perpendicular bisector of the line segment AB is
  A)
             \[2x+3y=18\]                          done clear
  B)
             \[2x-3y+18=0\] done clear
  C)
             \[2x+3y-1=0\]                         done clear
  D)
             \[3x-2y+1=0\] done clear
  View Solution play_arrow

• question_answer15)
  If the coordinates of the points A, B, C be (-1, 5), (0, 0) and (2, 2) respectively and D be the middle point of BC, then the equation of the perpendicular drawn from B to the line AD is
  A)
  \[x+2y=0\]                               done clear
  B)
  \[2x+y=0\] done clear
  C)
  \[x-2y=0\]                                 done clear
  D)
  \[2x-y=0\] done clear
  View Solution play_arrow

• question_answer16)
  The equation of the line passing through the point \[({x}',\ {y}')\] and perpendicular to the line \[y{y}'=2a\,(x+{x}')\] is
  A)
             \[x{y}'+2ay+2a{y}'-{x}'{y}'=0\] done clear
  B)
             \[x{y}'+2ay-2a{y}'-{x}'{y}'=0\] done clear
  C)
             \[x{y}'+2ay+2a{y}'+{x}'{y}'=0\]                                           done clear
  D)
             \[x{y}'+2ay-2a{y}'+{x}'{y}'=0\] done clear
  View Solution play_arrow

• question_answer17)
  If the middle points of the sides BC, CA and AB of the triangle ABC be (1, 3), (5, 7) and (-5, 7), then the equation of the side AB is               
  A)
  \[x-y-2=0\]                                done clear
  B)
  \[x-y+12=0\] done clear
  C)
  \[x+y-12=0\]                           done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer18)
  If the coordinates of the vertices of the triangle ABC be (-1, 6), (-3, -9), and (5, -8) respectively, then the equation of the median through C is
  A)
  \[13x-14y-47=0\]                    done clear
  B)
  \[13x-14y+47=0\] done clear
  C)
  \[13x+14y+47=0\]                done clear
  D)
  \[13x+14y-47=0\] done clear
  View Solution play_arrow

• question_answer19)
  The equation of the line perpendicular to the line \[\frac{x}{a}-\frac{y}{b}=1\] and passing through the point at which it cuts x-axis, is [RPET 1996; Kerala (Engg.) 2002]
  A)
  \[\frac{x}{a}+\frac{y}{b}+\frac{a}{b}=0\]                            done clear
  B)
  \[\frac{x}{b}+\frac{y}{a}=\frac{b}{a}\] done clear
  C)
  \[\frac{x}{b}+\frac{y}{a}=0\]\[\] done clear
  D)
  \[\frac{x}{b}+\frac{y}{a}=\frac{a}{b}\] done clear
  View Solution play_arrow

• question_answer20)
  The equation of the line passing through the point (1, 2) and perpendicular to the line \[x+y+1=0\] is                 [MNR 1981]
  A)
             \[y-x+1=0\]                              done clear
  B)
             \[y-x-1=0\] done clear
  C)
             \[y-x+2=0\]                              done clear
  D)
             \[y-x-2=0\] done clear
  View Solution play_arrow

• question_answer21)
  A line passes through the point (3, 4) and cuts off intercepts from the coordinates axes such that their sum is 14. The equation of the line is   
  A)
             \[4x-3y=24\]                            done clear
  B)
             \[4x+3y=24\] done clear
  C)
             \[3x-4y=24\]                            done clear
  D)
             \[3x+4y=24\] done clear
  View Solution play_arrow

• question_answer22)
  The equation of the line bisecting the line segment joining the points (a, b) and \[({a}',\ {b}')\]at right angle, is
  A)
             \[2(a-{a}')x+2(b-{b}')y={{a}^{2}}+{{b}^{2}}-{{{a}'}^{2}}-{{{b}'}^{2}}\] done clear
  B)
             \[(a-{a}')x+(b-{b}')y={{a}^{2}}+{{b}^{2}}-{{{a}'}^{2}}-{{{b}'}^{2}}\] done clear
  C)
             \[2(a-{a}')x+2(b-{b}')y={{{a}'}^{2}}+b{{'}^{2}}-{{a}^{2}}-{{b}^{2}}\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer23)
  The equations of the lines which pass through the origin and are inclined at an angle \[{{\tan }^{-1}}m\] to the line \[y=mx+c,\] are
  A)
             \[x=0,\ \ 2mx+({{m}^{2}}-1)\ y=0\]                                     done clear
  B)
             \[y=0,\ \ 2mx+({{m}^{2}}-1)\ y=0\] done clear
  C)
             \[y=0,\ \ 2mx+(1-{{m}^{2}})\ y=0\]                                     done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer24)
  A line meets x?axis and y-axis at the points A and B respectively. If the middle point of AB be \[({{x}_{1}},\ {{y}_{1}}),\]then the equation of the line is
  A)
             \[{{y}_{1}}x+{{x}_{1}}y=2{{x}_{1}}{{y}_{1}}\] done clear
  B)
             \[{{x}_{1}}x+{{y}_{1}}y=2{{x}_{1}}{{y}_{1}}\] done clear
  C)
             \[{{y}_{1}}x+{{x}_{1}}y={{x}_{1}}{{y}_{1}}\]              done clear
  D)
             \[{{x}_{1}}x+{{y}_{1}}y={{x}_{1}}{{y}_{1}}\] done clear
  View Solution play_arrow

• question_answer25)
  The equation of the line parallel to the line \[2x-3y=1\] and passing through the middle point of the line segment joining the points (1, 3) and (1, - 7), is
  A)
             \[2x-3y+8=0\]                         done clear
  B)
             \[2x-3y=8\] done clear
  C)
             \[2x-3y+4=0\]                         done clear
  D)
             \[2x-3y=4\] done clear
  View Solution play_arrow

• question_answer26)
  The equation of the lines which passes through the point (3, - 2) and are inclined at \[{{60}^{o}}\]to the line\[\sqrt{3}x+y=1\] [IIT 1974; MP PET 1996]
  A)
             \[y+2=0,\ \ \sqrt{3}x-y-2-3\sqrt{3}=0\] done clear
  B)
             \[x-2=0,\ \ \sqrt{3}x-y+2+3\sqrt{3}=0\] done clear
  C)
             \[\sqrt{3}x-y-2-3\sqrt{3}=0\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer27)
  The equations of the lines passing through the point (1, 0) and at a distance \[\frac{\sqrt{3}}{2}\] from the origin, are
  A)
             \[\sqrt{3}x+y-\sqrt{3}=0,\ \ \sqrt{3}x-y-\sqrt{3}=0\] done clear
  B)
             \[\sqrt{3}x+y+\sqrt{3}=0,\ \ \sqrt{3}x-y+\sqrt{3}=0\] done clear
  C)
             \[x+\sqrt{3}y-\sqrt{3}=0,\ \ x-\sqrt{3}y-\sqrt{3}=0\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer28)
  The equation of a straight line passing through \[x+2y=2\]and cutting an intercept equal in magnitude but opposite in sign from the axes is given by          [RPET 1984; MP PET 1993]
  A)
             \[x-y+5=0\]                              done clear
  B)
             \[x+y-5=0\] done clear
  C)
             \[x-y-5=0\]                                done clear
  D)
             \[x+y+5=0\] done clear
  View Solution play_arrow

• question_answer29)
  The equation of a line passing through the point of intersection of the lines \[x+5y+7=0,\ \ 3x+2y-5=0,\] and perpendicular to the line \[7x+2y-5=0,\] is given by  [RPET 1987; MP PET 1993; Pb. CET 2000]
  A)
             \[2x-7y-20=0\]                         done clear
  B)
             \[2x+7y-20=0\] done clear
  C)
             \[-2x+7y-20=0\]                     done clear
  D)
             \[2x+7y+20=0\] done clear
  View Solution play_arrow

• question_answer30)
  A line passes through the point of intersection of \[2x+y=5\] and \[x+3y+8=0\] and parallel to the line \[3x+4y=7\] is   [RPET 1984; MP PET 1991]
  A)
             \[3x+4y+3=0\]                       done clear
  B)
             \[3x+4y=0\] done clear
  C)
             \[4x-3y+3=0\]                         done clear
  D)
             \[4x-3y=3\] done clear
  View Solution play_arrow

• question_answer31)
  The equation of the line joining the origin to the point (-4, 5), is                                           [MP PET 1984]
  A)
  \[5x+4y=0\]                             done clear
  B)
  \[3x+4y=2\] done clear
  C)
  \[5x-4y=0\]                               done clear
  D)
  \[4x-5y=0\] done clear
  View Solution play_arrow

• question_answer32)
  The equation of the line which cuts off an intercept 3 units on OX and an intercept -2 unit on OY, is     [MP PET 1984]
  A)
  \[\frac{x}{3}-\frac{y}{2}=1\] done clear
  B)
  \[\frac{x}{3}+\frac{y}{2}=1\] done clear
  C)
  \[\frac{x}{2}+\frac{y}{3}=1\]      done clear
  D)
  \[\frac{x}{2}-\frac{y}{3}=1\] done clear
  View Solution play_arrow

• question_answer33)
  The equation of a line through \[(3,\,-4)\] and perpendicular to the line \[3x+4y=5\]is   [RPET 1981, 84, 86; MP PET 1984]
  A)
             \[4x+3y=24\]                          done clear
  B)
             \[y-4=(x+3)\] done clear
  C)
             \[3y-4x=24\]                            done clear
  D)
             \[y+4=\frac{4}{3}(x-3)\] done clear
  View Solution play_arrow

• question_answer34)
  Equation of the line passing through (1, 2) and parallel to the line \[y=3x-1\]is                                          [MP PET 1984]
  A)
             \[y+2=x+1\]                            done clear
  B)
             \[y+2=3(x+1)\] done clear
  C)
             \[y-2=3(x-1)\]                           done clear
  D)
             \[y-2=x-1\] done clear
  View Solution play_arrow

• question_answer35)
  Equation of the line passing through (-1,1) and perpendicular to the line \[4/\sqrt{15}\]is        [MP PET 1984]
  A)
  \[2(y-1)=3(x+1)\]                    done clear
  B)
  \[3(y-1)=-\ 2(x+1)\] done clear
  C)
  \[y-1=2(x+1)\]                         done clear
  D)
  \[3(y-1)=x+1\] done clear
  View Solution play_arrow

• question_answer36)
  The equation of a line through the intersection of lines \[x=0\] and \[y=0\]and through the point (2, 2), is  [MP PET 1984]
  A)
             \[y=x-1\]                                   done clear
  B)
             \[y=-x\] done clear
  C)
             \[y=x\]                                       done clear
  D)
             \[y=-x+2\] done clear
  View Solution play_arrow

• question_answer37)
  Equation of a line through the origin and perpendicular to, the line joining (a, 0) and (- a, 0), is              [MP PET 1984]
  A)
  \[y=0\]                                       done clear
  B)
  \[x=0\] done clear
  C)
  \[x=-\ a\]                                    done clear
  D)
  \[y=-\ a\] done clear
  View Solution play_arrow

• question_answer38)
  For specifying a straight line how many geometrical parameters should be known                                     [MP PET 1982]
  A)
             1     done clear
  B)
             2 done clear
  C)
             4     done clear
  D)
             3 done clear
  View Solution play_arrow

• question_answer39)
  The points A (1, 3) and C (5, 1) are the opposite vertices of rectangle. The equation of line passing through other two vertices and of gradient 2, is                                                               [RPET 1991]
  A)
             \[2x+y-8=0\]                           done clear
  B)
             \[2x-y-4=0\]                             done clear
  C)
             \[2x-y+4=0\]                           done clear
  D)
             \[2x+y+7=0\] done clear
  View Solution play_arrow

• question_answer40)
  The intercept cut off from y?axis is twice that from x?axis by the line and line is passes through (1, 2) then its equation is    [AMU 1972; RPET 1985]
  A)
             \[2x+y=4\]                               done clear
  B)
             \[2x+y+4=0\] done clear
  C)
             \[2x-y=4\]                                 done clear
  D)
             \[2x-y+4=0\] done clear
  View Solution play_arrow

• question_answer41)
  The equation of line, which bisect the line joining two points (2, -19) and (6, 1) and perpendicular to the line joining two points (-1, 3) and (5, - 1), is           [RPET 1987]
  A)
  \[3x-2y=30\]                            done clear
  B)
  \[2x-y-3=0\] done clear
  C)
  \[2x+3y=20\]                          done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer42)
  The equation of line whose mid point is \[({{x}_{1}},\ {{y}_{1}})\] in between the axes, is                                    [RPET 1988]
  A)
              \[\frac{x}{{{x}_{1}}}+\frac{y}{{{y}_{1}}}=2\]                 done clear
  B)
             \[\frac{x}{{{x}_{1}}}+\frac{y}{{{y}_{1}}}=\frac{1}{2}\] done clear
  C)
             \[\frac{x}{{{x}_{1}}}+\frac{y}{{{y}_{1}}}=1\]                  done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer43)
  The equation of line passing through (c, d) and  parallel to \[ax+by+c=0,\]is                                             [RPET 1987]
  A)
             \[a(x+c)+b\,(y+d)=0\]           done clear
  B)
             \[a(x+c)-b(y+d)=0\] done clear
  C)
             \[a(x-c)+b(y-d)=0\]                 done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer44)
  The equation of line passing through point of intersection of lines \[3x-2y-1=0\] and \[x-4y+3=0\]and the point \[(\pi ,\ 0),\] is [RPET 1987]
  A)
             \[x-y=\pi \]                                done clear
  B)
             \[x-y=\pi (y+1)\] done clear
  C)
             \[x-y=\pi (1-y)\]                        done clear
  D)
             \[x+y=\pi (1-y)\] done clear
  View Solution play_arrow

• question_answer45)
  A line perpendicular to the line \[ax+by+c=0\] and passes through \[(a,\ b).\] The equation of the line is  [RPET 1988; MP PET 1995]
  A)
             \[bx-ay+({{a}^{2}}-{{b}^{2}})=0\]                                  done clear
  B)
             \[bx-ay-({{a}^{2}}-{{b}^{2}})=0\] done clear
  C)
             \[bx-ay=0\]                               done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer46)
  The equation of line passing through the point of intersection of the lines \[4x-3y-1=0\]and \[5x-2y-3=0\] and parallel to the line \[2y-3x+2=0,\] is                                                            [RPET 1985, 86, 88]
  A)
             \[x-3y=1\]                                 done clear
  B)
             \[3x-2y=1\]                               done clear
  C)
             \[2x-3y=1\]                               done clear
  D)
             \[2x-y=1\] done clear
  View Solution play_arrow

• question_answer47)
  The equation of the line passing through (4, -6) and makes an angle \[{{45}^{o}}\]with positive x-axis, is       [RPET 1984]
  A)
  \[x-y-10=0\]                             done clear
  B)
  \[x-2y-16=0\] done clear
  C)
  \[x-3y-22=0\]                           done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer48)
  The equation of the line passes through \[(a,\ b)\]and parallel to the line \[\frac{x}{a}+\frac{y}{b}=1,\]is                                             [RPET 1986, 95]
  A)
             \[\frac{x}{a}+\frac{y}{b}=3\]       done clear
  B)
             \[\frac{x}{a}+\frac{y}{b}=2\]       done clear
  C)
             \[\frac{x}{a}+\frac{y}{b}=0\]       done clear
  D)
             \[\frac{x}{a}+\frac{y}{b}+2=0\] done clear
  View Solution play_arrow

• question_answer49)
  Equation of the hour hand at 4 O? clock is
  A)
             \[x-\sqrt{3}\ y=0\]                    done clear
  B)
             \[\sqrt{3}\ x-y=0\] done clear
  C)
             \[x+\sqrt{3}\ y=0\]                  done clear
  D)
             \[\sqrt{3}\ x+y=0\] done clear
  View Solution play_arrow

• question_answer50)
  Equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of \[{{120}^{o}}\]with the x?axis, is                                                       [MNR 1986]
  A)
             \[x\sqrt{3}+y+8=0\]              done clear
  B)
             \[x\sqrt{3}-y=8\] done clear
  C)
             \[x\sqrt{3}-y=8\]                      done clear
  D)
             \[x-\sqrt{3}\ y+8=0\] done clear
  View Solution play_arrow

• question_answer51)
  The straight line passes through the point of inter -section of the straight lines \[x+2y-10=0\] and \[2x+y+5=0,\] is   [IIT 1983]
  A)
             \[5x-4y=0\]                               done clear
  B)
             \[5x+4y=0\]                             done clear
  C)
             \[4x-5y=0\]                               done clear
  D)
             \[4x+5y=0\] done clear
  View Solution play_arrow

• question_answer52)
  The equation to the straight line passing through the point \[(a{{\cos }^{3}}\theta ,\ a{{\sin }^{3}}\theta )\] and perpendicular to the line \[x\sec \theta +y\,\text{cosec}\,\theta =a,\] is                                                                 [AMU 1975]
  A)
             \[x\cos \theta -y\sin \theta =a\cos \ 2\theta \] done clear
  B)
             \[x\cos \theta +y\sin \theta =a\cos \ 2\theta \] done clear
  C)
             \[x\sin \theta +y\cos \theta =a\cos \ 2\theta \]                            done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer53)
  Equation of the perpendicular bisector of the line segment joining the points (7, 4) and (-1, -2), is       [AMU 1979]
  A)
  \[4x-3y=15\]                            done clear
  B)
  \[3x+4y=15\] done clear
  C)
  \[4x+3y=15\]                          done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer54)
  Equations of the two straight lines passing through the point (3, 2) and making an angle of \[{{45}^{o}}\]with the line \[x-2y=3,\] are [AMU 1978]
  A)
             \[3x+y+7=0\] and \[x+3y+9=0\] done clear
  B)
             \[3x-y-7=0\] and \[x+3y-9=0\] done clear
  C)
             \[x+3y-7=0\] and \[x+3y-9=0\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer55)
  Equations of lines which passes through the points of intersection of the lines \[4x-3y-1=0\] and \[2x-5y+3=0\] and are equally inclined to the axes are     [AMU 1981]
  A)
             \[y\pm x=0\]                             done clear
  B)
             \[y-1=\pm \ 1(x-1)\] done clear
  C)
             \[x-1=\pm \ 2(y-1)\]                 done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer56)
  The equations of two lines through \[(0,\ a)\]which are at distance ?a? from the point \[(2a,\ 2a)\]are  [Dhanbad Engg. 1972]
  A)
             \[y-a=0\] and \[4x-3y-3a=0\] done clear
  B)
             \[y-a=0\] and \[3x-4y+3a=0\] done clear
  C)
             \[y-a=0\] and \[4x-3y+3a=0\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer57)
  A line is such that its segment between the straight lines \[5x-y-4=0\] and \[3x+4y-4=0\] is bisected at the point (1, 5), then its equation is                        [Roorkee 1988]
  A)
             \[83x-35y+92=0\]                  done clear
  B)
             \[35x-83y+92=0\] done clear
  C)
             \[35x+35y+92=0\]                done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer58)
  Equation of the line which passes through the point \[(-4,\ 3)\] and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point, is                           [AMU 1973;  Dhanbad Engg. 1971]        
  A)
             \[9x+20y+96=0\]                  done clear
  B)
             \[20x+9y+96=0\] done clear
  C)
             \[9x-20y+96=0\]                    done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer59)
  The equation of a straight line passing through the points \[(-5,\ -6)\] and (3, 10), is                                  [MNR 1974]
  A)
             \[x-2y=4\]                                 done clear
  B)
             \[2x-y+4=0\] done clear
  C)
             \[2x+y=4\]                               done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer60)
  The equations of the lines through the point of intersection of the lines \[x-y+1=0\] and \[2x-3y+5=0\] and whose distance from the point (3, 2) is \[\frac{7}{5},\]is                               [IIT 1963]
  A)
             \[3x-4y-6=0\] and \[4x+3y+1=0\] done clear
  B)
             \[3x-4y+6=0\] and \[4x-3y-1=0\] done clear
  C)
             \[3x-4y+6=0\] and \[4x-3y+1=0\] done clear
  D)
             None of these                           done clear
  View Solution play_arrow

• question_answer61)
  The equation of the line which cuts off the intercepts \[2a\sec \theta \] and \[2a\,\text{cosec}\,\theta \] on the axes is
  A)
             \[x\sin \theta +y\cos \theta -2a=0\]                                            done clear
  B)
             \[x\cos \theta +y\sin \theta -2a=0\]                                            done clear
  C)
             \[x\sec \theta +y\,\text{cosec}\theta -2a=0\]                             done clear
  D)
             \[x\,\text{cosec}\theta +y\sec \theta -2a=0\] done clear
  View Solution play_arrow

• question_answer62)
  If the equation \[y=mx+c\] and \[x\cos \alpha +y\sin \alpha =p\] represents the same straight line, then
  A)
             \[p=c\sqrt{1+{{m}^{2}}}\]        done clear
  B)
             \[c=p\sqrt{1+{{m}^{2}}}\]        done clear
  C)
             \[cp=\sqrt{1+{{m}^{2}}}\]        done clear
  D)
                  \[{{p}^{2}}+{{c}^{2}}+{{m}^{2}}=1\] done clear
  View Solution play_arrow

• question_answer63)
  The equation to the straight line passing through the point of intersection of the lines \[5x-6y-1=0\] and \[3x+2y+5=0\] and perpendicular to the line \[3x-5y+11=0\] is  [MP PET 1994]
  A)
             \[5x+3y+8=0\]                       done clear
  B)
             \[3x-5y+8=0\] done clear
  C)
             \[5x+3y+11=0\]                     done clear
  D)
             \[3x-5y+11=0\] done clear
  View Solution play_arrow

• question_answer64)
  Line passing through (1, 2) and (2, 5) is                       [RPET 1995]
  A)
             \[3x-y+1=0\]                           done clear
  B)
             \[3x+y+1=0\] done clear
  C)
             \[y-3x+1=0\]                           done clear
  D)
             \[3x+y-1=0\] done clear
  View Solution play_arrow

• question_answer65)
  Equation of line passing through (1, 2) and perpendicular to \[3x+4y+5=0\] is                                        [RPET 1995]
  A)
             \[3y=4x-2\]                               done clear
  B)
             \[3y=4x+3\] done clear
  C)
             \[3y=4x+4\]                             done clear
  D)
             \[3y=4x+2\] done clear
  View Solution play_arrow

• question_answer66)
  The number of lines that are parallel to \[2x+6y+7=0\] and have an intercept of length 10 between the coordinate axes is
  A)
             1     done clear
  B)
             2 done clear
  C)
             4     done clear
  D)
             Infinitely many done clear
  View Solution play_arrow

• question_answer67)
  A line passes through (2, 2) and is perpendicular to the line \[3x+y=3.\] Its y?intercept is                        [IIT Screening 1992]
  A)
             \[1/3\]                                         done clear
  B)
             \[2/3\] done clear
  C)
             1     done clear
  D)
             \[4/3\] done clear
  View Solution play_arrow

• question_answer68)
  A straight the makes an angle of \[{{135}^{o}}\]with the x-axis and cuts y-axis at a distance -5 from the origin. The equation of the line is [MP PET 1998]
  A)
  \[2x+y+5=0\]                         done clear
  B)
  \[x+2y+3=0\] done clear
  C)
  \[x+y+5=0\]                            done clear
  D)
  \[x+y+3=0\] done clear
  View Solution play_arrow

• question_answer69)
  A straight line through P(1, 2) is such that its intercept between the axes is bisected at P. Its equation is  [EAMCET 1994]
  A)
             \[x+2y=5\]                               done clear
  B)
             \[x-y+1=0\] done clear
  C)
             \[x+y-3=0\]                              done clear
  D)
             \[2x+y-4=0\] done clear
  View Solution play_arrow

• question_answer70)
  The equation of the straight line joining the point \[(a,\ b)\]to the point of intersection of the lines \[\frac{x}{a}+\frac{y}{b}=1\] and \[\frac{x}{b}+\frac{y}{a}=1\] is
  A)
             \[{{a}^{2}}y-{{b}^{2}}x=ab\ (a-b)\]                                  done clear
  B)
             \[{{a}^{2}}y+{{b}^{2}}y=ab\ (a+b)\] done clear
  C)
             \[{{a}^{2}}y+{{b}^{2}}x=ab\]                                          done clear
  D)
             \[{{a}^{2}}x+{{b}^{2}}y=ab\ (a-b)\] done clear
  View Solution play_arrow

• question_answer71)
  The equations of the lines through the origin making an angle of \[{{60}^{o}}\] with the line \[x+y\sqrt{3}+3\sqrt{3}=0\] are
  A)
             \[y=0,\ x-y\sqrt{3}=0\]           done clear
  B)
             \[x=0,\ x-y\sqrt{3}=0\] done clear
  C)
             \[x=0,\ x+y\sqrt{3}=0\]         done clear
  D)
             \[y=0,\ x+y\sqrt{3}=0\] done clear
  View Solution play_arrow

• question_answer72)
  The point \[P\,(a,\ b)\]lies on the straight line \[3x+2y=13\] and the point \[Q\ (b,\ a)\] lies on the straight line \[4x-y=5,\]then the equation of line PQ is                                                     [MP PET 1999]
  A)
             \[x-y=5\]                                   done clear
  B)
             \[x+y=5\] done clear
  C)
             \[x+y=-\ 5\]                              done clear
  D)
             \[x-y=-\ 5\] done clear
  View Solution play_arrow

• question_answer73)
  The equation of the line passing through (1, 1) and parallel to the line \[2x+3y-7=0\] is                                         [RPET 1996]
  A)
             \[2x+3y-5=0\]                         done clear
  B)
             \[3x+2y-5=0\] done clear
  C)
             \[3x-2y-7=0\]                           done clear
  D)
             \[2x+3y+5=0\] done clear
  View Solution play_arrow

• question_answer74)
  If the intercept made by the line between the axis is bisected at the point (5, 2), then its equation is         [RPET 1996]
  A)
             \[5x+2y=20\]                          done clear
  B)
             \[2x+5y=20\]                          done clear
  C)
             \[5x-2y=20\]                            done clear
  D)
             \[2x-5y=20\] done clear
  View Solution play_arrow

• question_answer75)
  The equation of straight line passing through the intersection of the lines \[x-2y=1\] and \[x+3y=2\] and parallel to \[3x+4y=0\] is [MP PET 2000]
  A)
             \[3x+4y+5=0\]                       done clear
  B)
             \[3x+4y-10=0\] done clear
  C)
             \[3x+4y-5=0\]                         done clear
  D)
             \[3x+4y+6=0\] done clear
  View Solution play_arrow

• question_answer76)
  Equation of a line passing through the point of intersection of lines \[2x-3y+4=0,\] \[3x+4y-5=0\] and perpendicular to \[6x-7y+3=0,\] then its equation is                                           [RPET 2000]
  A)
             \[119x+102y+125=0\]         done clear
  B)
             \[119x+102y=125\]               done clear
  C)
             \[119x-102y=125\]                 done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer77)
  If we reduce \[3x+3y+7=0\] to the form \[x\cos \alpha +y\sin \alpha =p,\] then the value of p is            [MP PET 2001]
  A)
             \[\frac{7}{2\sqrt{3}}\]             done clear
  B)
             \[\frac{7}{3}\] done clear
  C)
             \[\frac{3\sqrt{7}}{2}\]             done clear
  D)
             \[\frac{7}{3\sqrt{2}}\] done clear
  View Solution play_arrow

• question_answer78)
  The equation of the straight line joining the origin to the point of intersection of \[y-x+7=0\] and \[y+2x-2=0\] is [MP PET 2001]
  A)
             \[3x+4y=0\]                             done clear
  B)
             \[3x-4y=0\] done clear
  C)
             \[4x-3y=0\]                               done clear
  D)
             \[4x+3y=0\] done clear
  View Solution play_arrow

• question_answer79)
  The equation of line perpendicular to \[x=c\]is            [RPET 2001]
  A)
             \[y=d\]                                       done clear
  B)
             \[x=d\] done clear
  C)
             \[x=0\]                                       done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer80)
  A line AB makes zero intercepts on x?axis and    y?axis and it is perpendicular to another line CD, \[3x+4y+6=0.\] The equation of line AB is                                                               [Karnataka CET 2001]
  A)
             \[y=4\]                                       done clear
  B)
             \[4x-3y+8=0\] done clear
  C)
             \[4x-3y=0\]                               done clear
  D)
             \[4x-3y+6=0\] done clear
  View Solution play_arrow

• question_answer81)
  The equation of straight line passing through point of intersection of the straight lines \[3x-y+2=0\] and \[5x-2y+7=0\] and having infinite slope is [UPSEAT 2001]
  A)
             \[x=2\]                                       done clear
  B)
             \[x+y=3\] done clear
  C)
             \[x=3\]                                       done clear
  D)
             \[x=4\] done clear
  View Solution play_arrow

• question_answer82)
  The equation of the straight line which is perpendicular to \[y=x\] and passes through (3, 2) is            [MP PET 2002]
  A)
             \[x-y=5\]                                   done clear
  B)
             \[x+y=5\] done clear
  C)
             \[x+y=1\]                                 done clear
  D)
             \[x-y=1\] done clear
  View Solution play_arrow

• question_answer83)
  Equation to the straight line cutting off an intercept 2 from the negative direction of the axis of y and inclined at 30o to the positive direction of axis of x, is        [MP PET 2003]
  A)
             \[y+x-\sqrt{3}=0\]                  done clear
  B)
             \[y-x+2=0\] done clear
  C)
             \[y-\sqrt{3}\,x-2=0\]                done clear
  D)
             \[\sqrt{3}y-x+2\sqrt{3}=0\] done clear
  View Solution play_arrow

• question_answer84)
  The line passing through \[(-1,\pi /2)\] and perpendicular to \[\sqrt{3}\sin \theta +2\cos \theta =\frac{4}{r}\] is                                     [EAMCET 2003]
  A)
             \[2=\sqrt{3}\,r\cos \theta -2\,r\sin \theta \]                                 done clear
  B)
             \[5=-2\sqrt{3}\,r\sin \theta +4\,r\cos \theta \] done clear
  C)
             \[2=\sqrt{3}\,r\cos \theta +2\,r\cos \theta \] done clear
  D)
             \[5=2\sqrt{3}\,r\sin \theta +4\,r\cos \theta \]                             done clear
  View Solution play_arrow

• question_answer85)
  The equation of the line bisecting perpendicularly the segment joining the points (? 4, 6) and (8, 8) is [Karnataka CET 2003]
  A)
             \[6x+y-19=0\]                         done clear
  B)
             \[y=7\] done clear
  C)
             \[6x+2y-19=0\]                       done clear
  D)
             \[x+2y-7=0\] done clear
  View Solution play_arrow

• question_answer86)
  Equation of a line passing through (1, -2) and perpendicular to the line \[3x-5y+7=0\] is                                       [RPET 2003]
  A)
  \[5x+3y+1=0\]                       done clear
  B)
  \[3x+5y+1=0\] done clear
  C)
  \[5x-3y-1=0\]                           done clear
  D)
  \[3x-5y+1=0\] done clear
  View Solution play_arrow

• question_answer87)
  If the line \[\frac{x}{a}+\frac{y}{b}=1\] passes through the points (2, -3) and (4, -5), then \[(a,\ b)\]=
  A)
  (1, 1)                                          done clear
  B)
  (- 1, 1) done clear
  C)
  (1, - 1)                                       done clear
  D)
  (- 1, - 1) done clear
  View Solution play_arrow

• question_answer88)
  If the slope of a line passing through the point  A (3, 2) be 3/4, then the points on the line which are 5 units away from A, are [IIT 1965]
  A)
             (5, 5), (- 1, - 1)                          done clear
  B)
             (7, 5), (- 1, - 1) done clear
  C)
             (5, 7), (- 1, - 1)                          done clear
  D)
             (7, 5), (1, 1)                              done clear
  View Solution play_arrow

• question_answer89)
  For the lines \[2x+5y=7\]and \[2x-5y=9,\]which of the following statement is true 
  A)
             Lines are parallel                      done clear
  B)
             Lines are coincident done clear
  C)
             Lines are intersecting               done clear
  D)
             Lines are perpendicular          done clear
  View Solution play_arrow

• question_answer90)
  The opposite angular points of a square are \[(3,\ 4)\] and \[(1,\ -\ 1)\]. Then the co-ordinates of other two points are  [Roorkee 1985]
  A)
             \[D\,\left( \frac{1}{2},\,\,\frac{9}{2} \right)\,,\,\,B\,\left( -\frac{1}{2},\,\,\frac{5}{2} \right)\]               done clear
  B)
             \[D\,\left( \frac{1}{2},\,\,\frac{9}{2} \right)\,,\,\,B\,\left( \frac{1}{2},\,\,\frac{5}{2} \right)\] done clear
  C)
             \[D\,\left( \frac{9}{2},\,\,\frac{1}{2} \right)\,,\,\,B\,\left( -\frac{1}{2},\,\,\frac{5}{2} \right)\]               done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer91)
  Two consecutive sides of a parallelogram are \[4x+5y=0\] and \[7x+2y=0.\] If the equation to one diagonal is \[11x+7y=9,\] then the equation of the other diagonal is                                                        [IIT 1970]
  A)
             \[x+2y=0\]                               done clear
  B)
             \[2x+y=0\] done clear
  C)
             \[x-y=0\]                                   done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer92)
  One diagonal of a square is along the line \[8x-15y=0\] and one of its vertex is (1, 2). Then the equation of the sides of the square passing through this vertex, are                       [IIT 1962]
  A)
             \[23x+7y=9,\ 7x+23y=53\] done clear
  B)
             \[23x-7y+9=0,\ 7x+23y+53=0\] done clear
  C)
             \[23x-7y-9=0,\ 7x+23y-53=0\] done clear
  D)
             None of these                           done clear
  View Solution play_arrow

• question_answer93)
  The opposite vertices of a square are (1, 2) and (3, 8), then the equation of a diagonal of the square passing through the point (1, 2), is                             [Roorkee 1981]
  A)
             \[3x-y-1=0\]                             done clear
  B)
             \[3y-x-1=0\] done clear
  C)
             \[3x+y+1=0\]                         done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer94)
  The ends of the base of an isosceles triangle are at \[(2a,\ 0)\]and\[(0,\ a).\] The equation of one side is \[(lx+my)(a+b)=(l+m)\ ab\] The equation of the other side is
  A)
             \[x+2y-a=0\]                            done clear
  B)
             \[x+2y=2a\] done clear
  C)
             \[3x+4y-4a=0\]                       done clear
  D)
             \[3x-4y+4a=0\] done clear
  View Solution play_arrow

• question_answer95)
  The equation of the lines on which the perpendiculars from the origin make \[{{30}^{o}}\]angle with x?axis and which form a triangle of area \[\frac{50}{\sqrt{3}}\] with axes, are
  A)
             \[x+\sqrt{3}y\pm 10=0\]       done clear
  B)
             \[\sqrt{3}x+y\pm 10=0\] done clear
  C)
             \[x\pm \sqrt{3}y-10=0\]         done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer96)
  The base BC of a triangle ABC is bisected at the point (p, q) and the equations to the sides AB and AC are respectively \[x+y+3=0\] and \[qx+py=1.\] Then the equation to the median through A is
  A)
             \[2x-y=9\] done clear
  B)
             \[({{p}^{2}}+{{q}^{2}}-1)(px+qy-1)=(2p-1)(qx+py-1)\] done clear
  C)
             \[(pq-1)(px+qy-1)=({{p}^{2}}+{{q}^{2}}-1)(qx+py-1)\] done clear
  D)
             None of these                           done clear
  View Solution play_arrow

• question_answer97)
  The equation of the line which makes right angled triangle with axes whose area is 6 sq. units and whose hypotenuse is of 5 units, is 
  A)
             \[\frac{x}{4}+\frac{y}{3}=\pm \ 1\]                                         done clear
  B)
             \[\frac{x}{4}-\frac{y}{3}=\pm \ 3\] done clear
  C)
             \[\frac{x}{6}+\frac{y}{1}=\pm \ 1\]                                         done clear
  D)
             \[\frac{x}{1}-\frac{y}{6}=\pm \ 1\] done clear
  View Solution play_arrow

• question_answer98)
  A(-1, 1), B(5, 3) are opposite vertices of a square in xy-plane. The equation of the other diagonal (not passing through (A, B) of the square is given by    [EAMCET 1993]
  A)
  \[x-3y+4=0\]                           done clear
  B)
  \[2x-y+3=0\] done clear
  C)
  \[y+3x-8=0\]                           done clear
  D)
  \[x+2y-1=0\] done clear
  View Solution play_arrow

• question_answer99)
  In an isosceles triangle ABC, the coordinates of the points B and C on the base BC are respectively (1, 2) and (2, 1). If the equation of the line AB is \[y=2x\], then the  equation of the line AC is                                                                [Roorkee 2000]
  A)
             \[y=\frac{1}{2}(x-1)\]             done clear
  B)
             \[y=\frac{x}{2}\] done clear
  C)
             \[y=x-1\]                                   done clear
  D)
             \[2y=x+3\] done clear
  View Solution play_arrow

• question_answer100)
  Equations of diagonals of square formed by lines \[x=0,\] \[y=0,\]\[x=1\] and \[y=1\]are                                         [MP PET 1984]
  A)
             \[y=x,\ y+x=1\]                       done clear
  B)
             \[y=x,\ x+y=2\] done clear
  C)
             \[2y=x,\ y+x=\frac{1}{3}\]   done clear
  D)
             \[y=2x,\ y+2x=1\] done clear
  View Solution play_arrow

• question_answer101)
  The diagonal passing through origin of a quadrilateral formed by \[x=0,\ y=0,\ x+y=1\] and \[6x+y=3,\] is [IIT 1973]
  A)
             \[3x-2y=0\]                               done clear
  B)
             \[2x-3y=0\] done clear
  C)
             \[3x+2y=0\]                             done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer102)
  The vertices of a triangle OBC are \[(0,\ 0),\ (-3,\ -1)\] and \[(-1,\ -3)\ \]respectively. Then the equation of line parallel to BC which is at \[\frac{1}{2}\]unit distant from origin and cuts OB and OC, is                                       [IIT 1976]
  A)
             \[2x+2y+\sqrt{2}=0\]            done clear
  B)
             \[2x+2y-\sqrt{2}=0\] done clear
  C)
             \[2x-2y+\sqrt{2}=0\]              done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer103)
  A vertex of square is (3, 4) and diagonal \[x+2y=1,\] then the second diagonal which passes through given vertex will be
  A)
             \[2x-y+2=0\]                           done clear
  B)
             \[x+2y=11\] done clear
  C)
             \[2x-y=2\]                                 done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer104)
  A vertex of equilateral triangle is (2, 3) and equation of opposite side is \[x+y=2,\] then the equation of one side from rest two, is [IIT 1975]
  A)
             \[y-3=2(x-2)\]                           done clear
  B)
             \[y-3=(2-\sqrt{3})(x-2)\] done clear
  C)
             \[y-3=(\sqrt{3}-1)(x-2)\]         done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer105)
  A straight line moves so that the sum of the reciprocals of its intercepts on two perpendicular lines is constant, then the line passes through                        [IIT 1977]
  A)
             A fixed point                             done clear
  B)
             A variable point done clear
  C)
             Origin                                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer106)
  If a, b, c are in harmonic progression, then straight line \[\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0\] always passes through a fixed point, that point is [MP PET 1999; AIEEE 2005]
  A)
             \[(-1,\ -2)\]                                 done clear
  B)
             \[(-1,\ 2)\] done clear
  C)
             \[(1,\ -2)\]                                   done clear
  D)
             \[(1,\ -1/2)\] done clear
  View Solution play_arrow

• question_answer107)
  If the straight line \[ax+by+c=0\] always passes through      (1, -2), then a, b, c are                                  [AMU 2000]
  A)
  In A.P.                                        done clear
  B)
  In H.P. done clear
  C)
  In G.P.                                       done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer108)
  If \[u={{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0,\] \[v={{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] and  \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}},\] then the curve \[u+kv=0\]is        [MNR 1987]
  A)
             The same straight line u          done clear
  B)
             Different straight line done clear
  C)
             It is not a straight line               done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer109)
  For what values of a and b the intercepts cut off on the coordinate axes by the line \[ax+by+8=0\] are equal in length but opposite in signs to those cut off by the line \[2x-3y+6=0\] on the axes                 [MP PET 1983]  
  A)
             \[a=\frac{8}{3},\ b=-\ 4\]       done clear
  B)
             \[a=-\frac{8}{3},\ b=-\ 4\] done clear
  C)
             \[a=\frac{8}{3},\ b=4\]          done clear
  D)
             \[a=-\frac{8}{3},\ b=4\] done clear
  View Solution play_arrow

• question_answer110)
  If a and b are two arbitrary constants, then the straight line \[(a-2b)x+(a+3b)y+3a+4b=0\]will pass through [RPET 1990]
  A)
             \[(-1,\ -2)\]                                 done clear
  B)
             (1, 2) done clear
  C)
             \[(-2,\ -3)\]                                 done clear
  D)
             (2, 3) done clear
  View Solution play_arrow

• question_answer111)
  If \[a+b+c=0\] and \[p\ne 0,\] the lines \[ax+(b+c)y=p,\]  \[bx+(c+a)y=p\] and \[cx+(a+b)y=p\]
  A)
             Do not intersect                        done clear
  B)
             Intersect done clear
  C)
             Are concurrent                          done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer112)
  The symmetry in curve \[{{x}^{3}}+{{y}^{3}}=3axy\]along
  A)
  x-axis                                        done clear
  B)
  y-axis done clear
  C)
  Line y = x                                 done clear
  D)
  Opposite quadrants  done clear
  View Solution play_arrow

• question_answer113)
  The point of intersection of the lines \[\frac{x}{a}+\frac{y}{b}=1\] and \[\frac{x}{b}+\frac{y}{a}=1\] lies on the line
  A)
             \[x-y=0\]                                   done clear
  B)
             \[(x+y)(a+b)=2ab\] done clear
  C)
             \[(lx+my)(a+b)=(l+m)\ ab\]  done clear
  D)
             All of these done clear
  View Solution play_arrow

• question_answer114)
  The equations \[(b-c)x+(c-a)y+(a-b)=0\] and \[({{b}^{3}}-{{c}^{3}})x+({{c}^{3}}-{{a}^{3}})y+{{a}^{3}}-{{b}^{3}}=0\] will represent the same line, if
  A)
             b = c                                          done clear
  B)
             c = a done clear
  C)
             a = b                                         done clear
  D)
             a + b + c = 0 done clear
  E)
  (e)       All the above                            done clear
  View Solution play_arrow

• question_answer115)
  A straight line makes an angle of \[{{135}^{o}}\] with x-axis and cuts y-axis at a distance of -5 from the origin. The equation of the line is [Pb. CET 2001]
  A)
  \[2x+y+5=0\]                         done clear
  B)
  \[x+2y+3=0\] done clear
  C)
  \[x+y+5=0\]                            done clear
  D)
  \[x+y+3=0\] done clear
  View Solution play_arrow

• question_answer116)
  Equation of the straight line making equal intercepts on the axes and passing through the point (2, 4) is   [Karnataka CET 2004]
  A)
             \[4x-y-4=0\]                             done clear
  B)
             \[2x+y-8=0\] done clear
  C)
             \[x+y-6=0\]                              done clear
  D)
             \[x+2y-10=0\] done clear
  View Solution play_arrow

• question_answer117)
  The equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinate axes whose sum is ? 1 is [AIEEE 2004]
  A)
             \[\frac{x}{2}-\frac{y}{3}=1\]and\[\frac{x}{-2}+\frac{y}{1}=1\]      done clear
  B)
             \[\frac{x}{2}-\frac{y}{3}=-1\] and \[\frac{x}{-2}+\frac{y}{1}=-1\] done clear
  C)
             \[\frac{x}{2}-\frac{y}{3}=1\] and \[\frac{x}{2}+\frac{y}{1}=1\]     done clear
  D)
             \[\frac{\pi }{3}\] and \[\frac{x}{-2}+\frac{y}{1}=-1\] done clear
  View Solution play_arrow

• question_answer118)
  The line which is parallel to x?axis and crosses the curve \[y=\sqrt{x}\] at an angle of \[{{45}^{o}}\] is equal to                [Pb. CET 2002]
  A)
             \[x=\frac{1}{4}\]                     done clear
  B)
             \[y=\frac{1}{4}\] done clear
  C)
             \[y=\frac{1}{2}\]                     done clear
  D)
             \[y=1\] done clear
  View Solution play_arrow

• question_answer119)
  The equation of the line perpendicular to line \[ax+by+c=0\] and passing through \[(a,\ b)\]is equal to  [Pb. CET 2002]
  A)
             \[bx-ay=0\]                               done clear
  B)
             \[bx+ay-2ab=0\] done clear
  C)
             \[bx+ay=0\]                             done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer120)
  The points (1, 3) and (5, 1) are the opposite vertices of a rectangle. The other two vertices lie on the line \[y=2x+c,\] then the value of c will be                 [Pb. CET 2003; IIT 1981]
  A)
             4     done clear
  B)
             - 4 done clear
  C)
             2     done clear
  D)
             - 2 done clear
  View Solution play_arrow

• question_answer121)
  The triangle PQR is inscribed in the circle \[{{x}^{2}}+{{y}^{2}}=25\]. If Q and R have co-ordinates (3,4) and (? 4, 3) respectively, then \[\angle QPR\] is equal to                                  [IIT Screening 2000]
  A)
             \[\frac{\pi }{2}\]                        done clear
  B)
             \[\frac{\pi }{3}\] done clear
  C)
             \[\frac{\pi }{4}\]                        done clear
  D)
             \[\frac{\pi }{6}\] done clear
  View Solution play_arrow

• question_answer122)
  The point \[({{t}^{2}}+2t+5,\,2{{t}^{2}}+t-2)\] lies on the line \[x+y=2\] for
  A)
             All real values of t                     done clear
  B)
             Some real values of t done clear
  C)
             \[t=\frac{-3\pm \sqrt{3}}{6}\]       done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer123)
  The line joining the points (-1, 3) and (4, -2) will pass through the point (p, q) if
  A)
  \[p-q=1\]                                   done clear
  B)
  \[p+q=1\] done clear
  C)
  \[p-q=2\]                                   done clear
  D)
  \[p+q=2\] done clear
  View Solution play_arrow

• question_answer124)
  The line parallel to the x-axis and passing through the intersection of the lines \[ax+2by+3b=0\] and \[bx-2ay-3a=0\],  where \[(a,\,b)\ne (0,\,0)\] is         [AIEEE 2005]
  A)
             Above the x-axis at a distance of 3/2 from it done clear
  B)
             Above the x-axis at a distance of 2/3 from it done clear
  C)
             Below the x-axis at a distance of 3/2 from it done clear
  D)
             Below the x-axis at a distance of 2/3 from it done clear
  View Solution play_arrow

• question_answer125)
  Two points (a, 0) and (0, b) are joined by a straight line, Another point on this line is                                                [Orissa JEE 2005]
  A)
             \[(3a,-2b)\]                                done clear
  B)
             \[({{a}^{2}},ab)\] done clear
  C)
             \[(-3a,\,2b)\]                              done clear
  D)
             \[(a,\,b)\] done clear
  View Solution play_arrow

• question_answer126)
  The equation to the line bisecting the join of (3, -4) and (5, 2) and having its intercepts on the x-axis and the y-axis in the ratio 2 : 1 is       [Karnataka CET 2005]
  A)
  \[x+y-3=0\]                              done clear
  B)
  \[2x-y=9\] done clear
  C)
  \[x+2y=2\]                       done clear
  D)
  \[2x+y=7\] done clear
  View Solution play_arrow

• question_answer127)
  If  the co-ordinates of the points A and B be (1, 0) and \[(2,\sqrt{3})\], then the angle made by the line AB with x-axis is
  A)
             \[{{30}^{o}}\]                       done clear
  B)
             \[{{45}^{o}}\] done clear
  C)
             \[{{60}^{o}}\]                       done clear
  D)
             \[{{75}^{o}}\] done clear
  View Solution play_arrow

• question_answer128)
  The line \[lx+my+n=0\] will be parallel to x-axis, if
  A)
             \[l=m=0\]                                 done clear
  B)
             \[m=n=0\] done clear
  C)
             \[l=n=0\]                                  done clear
  D)
             \[l=0\] done clear
  View Solution play_arrow

• question_answer129)
  A line passing through origin and is perpendicular to two given lines \[2x+y+6=0\] and \[4x+2y-9=0\], then the ratio in which the origin divides this line is [DCE 2005]
  A)
             1 : 2                                           done clear
  B)
             2 : 1 done clear
  C)
             4 : 3 done clear
  D)
             3 : 4 done clear
  View Solution play_arrow