JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank

done Equation of Pair of Straight Lines Total Questions - 73

• question_answer1)
  The equation \[{{(x+y)}^{2}}-({{x}^{2}}+{{y}^{2}})=0\] represents
  A)
             A circle                                       done clear
  B)
             Two lines done clear
  C)
             Two parallel lines done clear
  D)
             Two mutually perpendicular lines done clear
  View Solution play_arrow

• question_answer2)
  If the slope of one of the lines represented by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] be the square of the other, then
  A)
             \[{{a}^{2}}b+a{{b}^{2}}-6abh+8{{h}^{3}}=0\] done clear
  B)
             \[{{a}^{2}}b+a{{b}^{2}}+6abh+8{{h}^{3}}=0\] done clear
  C)
             \[{{a}^{2}}b+a{{b}^{2}}-3abh+8{{h}^{3}}=0\] done clear
  D)
             \[{{a}^{2}}b+a{{b}^{2}}-6abh-8{{h}^{3}}=0\] done clear
  View Solution play_arrow

• question_answer3)
  Two lines represented by equation \[{{x}^{2}}+xy+{{y}^{2}}=0\] are
  A)
             Coincident                                  done clear
  B)
             Parallel done clear
  C)
             Mutually perpendicular             done clear
  D)
             Imaginary done clear
  View Solution play_arrow

• question_answer4)
  If the equation \[hxy+gx+fy+c=0\] represents a pair of straight lines, then
  A)
             \[fh=cg\]                                    done clear
  B)
             \[fg=ch\] done clear
  C)
             \[{{h}^{2}}=gf\]                          done clear
  D)
             \[fgh=c\] done clear
  View Solution play_arrow

• question_answer5)
  The equation of pair of straight lines perpendicular to the pair \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] is                                  [MP PET 1989]
  A)
             \[a{{x}^{2}}-2hxy+b{{y}^{2}}=0\] done clear
  B)
             \[b{{x}^{2}}+2hxy+a{{y}^{2}}=0\] done clear
  C)
             \[a{{y}^{2}}-2hxy+b{{x}^{2}}=0\]       done clear
  D)
             \[a{{y}^{2}}-b{{x}^{2}}=0\] done clear
  View Solution play_arrow

• question_answer6)
  The values of h for which the equation \[3{{x}^{2}}+2hxy-3{{y}^{2}}-40x+30y-75=0\] represents a pair of straight lines, are [MP PET 1989]
  A)
             4, 4  done clear
  B)
             4, 6 done clear
  C)
             4, - 4                                           done clear
  D)
             0, 4 done clear
  View Solution play_arrow

• question_answer7)
  The equation of lines passing through the origin and parallel to the lines \[y={{m}_{1}}x+{{c}_{1}}\] and \[y={{m}_{2}}x+{{c}_{2}}\] is
  A)
             \[{{m}_{1}}{{m}_{2}}{{x}^{2}}-({{m}_{1}}+{{m}_{2}})xy+{{y}^{2}}=0\] done clear
  B)
             \[{{m}_{1}}{{m}_{2}}{{x}^{2}}+({{m}_{1}}+{{m}_{2}})xy+{{y}^{2}}=0\] done clear
  C)
             \[{{m}_{1}}{{m}_{2}}{{y}^{2}}-({{m}_{1}}+{{m}_{2}})xy+{{x}^{2}}=0\] done clear
  D)
             \[{{m}_{1}}{{m}_{2}}{{y}^{2}}+({{m}_{1}}+{{m}_{2}})xy+{{x}^{2}}=0\] done clear
  View Solution play_arrow

• question_answer8)
  The equation of the lines represented by the equation \[ab({{x}^{2}}-{{y}^{2}})+({{a}^{2}}-{{b}^{2}})xy=0\] are
  A)
             \[ax-by=0,\ bx+ay=0\]               done clear
  B)
             \[ax-by=0,\ bx-ay=0\] done clear
  C)
             \[ax+by=0,\ bx+ay=0\]               done clear
  D)
             \[ax+by=0,\ bx-ay=0\] done clear
  View Solution play_arrow

• question_answer9)
  The equation \[{{(x-5)}^{2}}+(x-5)\,(y-6)\,-2\,{{(y-6)}^{2}}=0\] represents
  A)
             A circle done clear
  B)
             Two straight lines passing through origin done clear
  C)
             Two straight lines passing through the point (5, 6) done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer10)
  A second degree homogenous equation in x and y always represents
  A)
             A pair of straight lines done clear
  B)
             A circle done clear
  C)
             A conic section done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer11)
  If \[6{{x}^{2}}+11xy-10{{y}^{2}}+x+31y+k=0\] represents a pair of straight lines, then \[k=\]                                        [MP PET 1991]
  A)
             - 15                                            done clear
  B)
             6 done clear
  C)
             - 10 done clear
  D)
             - 4 done clear
  View Solution play_arrow

• question_answer12)
  If \[4ab=3{{h}^{2}}\], then the ratio of slopes of the lines represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] will be
  A)
             \[\sqrt{2}:1\]                        done clear
  B)
             \[\sqrt{3}:1\] done clear
  C)
             \[2:1\]                                      done clear
  D)
             \[1:3\] done clear
  View Solution play_arrow

• question_answer13)
  The lines represented by the equation \[a{{x}^{2}}(b-c)-xy(ab-bc)+c{{y}^{2}}(a-b)=0\] are
  A)
             \[a(b-c)x-c(a-b)y=0\], \[x+y=0\] done clear
  B)
             \[x+y=0\], \[x-y=0\] done clear
  C)
             \[a(b-c)x-c(a-b)y=0\], \[x-y=0\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer14)
  If the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] represents two lines \[y={{m}_{1}}x\] and \[y={{m}_{2}}x\], then         [CEE 1993; MP PET 1988]
  A)
             \[{{m}_{1}}+{{m}_{2}}=\frac{-2h}{b}\] and \[{{m}_{1}}{{m}_{2}}=\frac{a}{b}\] done clear
  B)
             \[{{m}_{1}}+{{m}_{2}}=\frac{2h}{b}\] and \[{{m}_{1}}{{m}_{2}}=\frac{-a}{b}\] done clear
  C)
             \[{{m}_{1}}+{{m}_{2}}=\frac{2h}{b}\] and \[{{m}_{1}}{{m}_{2}}=\frac{a}{b}\] done clear
  D)
                   \[{{m}_{1}}+{{m}_{2}}=\frac{2h}{b}\] and \[{{m}_{1}}{{m}_{2}}=-ab\] done clear
  View Solution play_arrow

• question_answer15)
  The nature of straight lines represented by the equation \[4{{x}^{2}}+12xy+9{{y}^{2}}=0\] is                                      [MP PET 1988]
  A)
             Real and coincident            done clear
  B)
             Real and different done clear
  C)
             Imaginary and different   done clear
  D)
             None of the above done clear
  View Solution play_arrow

• question_answer16)
  The equation of the perpendiculars drawn from the origin to the lines represented by the equation \[2{{x}^{2}}-10xy+12{{y}^{2}}+5x-16y-3=0\] is
  A)
             \[6{{x}^{2}}+5xy+{{y}^{2}}=0\]                                         done clear
  B)
             \[6{{y}^{2}}+5xy+{{x}^{2}}=0\] done clear
  C)
             \[6{{x}^{2}}-5xy+{{y}^{2}}=0\]                                          done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer17)
  Which of the following second degree equation represented a pair of straight lines                                         [MP PET 1990]
  A)
             \[{{x}^{2}}-xy-{{y}^{2}}=1\]    done clear
  B)
             \[-{{x}^{2}}+xy-{{y}^{2}}=1\] done clear
  C)
             \[4{{x}^{2}}-4xy+{{y}^{2}}=4\]                                          done clear
  D)
             \[{{x}^{2}}+{{y}^{2}}=4\] done clear
  View Solution play_arrow

• question_answer18)
  . The lines \[{{a}^{2}}{{x}^{2}}+bc{{y}^{2}}=a(b+c)xy\] will be coincident, if
  A)
             \[a=0\] or \[b=c\]               done clear
  B)
             \[a=b\] or \[a=c\] done clear
  C)
             \[c=0\] or \[a=b\]               done clear
  D)
             \[a=b+c\] done clear
  View Solution play_arrow

• question_answer19)
  If the equation \[2{{x}^{2}}-2hxy+2{{y}^{2}}=0\] represents two coincident straight lines passing through the origin, then \[h=\]
  A)
  \[\pm \text{ }6\] done clear
  B)
  \[\sqrt{6}\] done clear
  C)
  \[-\sqrt{6}\]                          done clear
  D)
  \[\pm \text{ }2\] done clear
  View Solution play_arrow

• question_answer20)
  If one of the lines represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] be \[y=mx\], then      [UPSEAT 1999]
  A)
             \[b{{m}^{2}}+2hm+a=0\]        done clear
  B)
             \[b{{m}^{2}}+2hm-a=0\] done clear
  C)
             \[a{{m}^{2}}+2hm+b=0\]        done clear
  D)
             \[b{{m}^{2}}-2hm+a=0\] done clear
  View Solution play_arrow

• question_answer21)
  The equation of the lines passing through the origin and parallel to the lines represented by the equation \[2{{x}^{2}}-xy-6{{y}^{2}}+7x+21y-15=0\], is
  A)
             \[2{{x}^{2}}-xy-6{{y}^{2}}=0\]                                           done clear
  B)
             \[6{{x}^{2}}-xy+2{{y}^{2}}=0\] done clear
  C)
             \[6{{x}^{2}}-xy-2{{y}^{2}}=0\]                                           done clear
  D)
             \[2{{x}^{2}}+xy-6{{y}^{2}}=0\] done clear
  View Solution play_arrow

• question_answer22)
  The equation \[2{{x}^{2}}+4xy-p{{y}^{2}}+4x+qy+1=0\] will represent two mutually perpendicular straight lines, if
  A)
             p = 1 and q = 2 or 6             done clear
  B)
             p = 2 and q = 0 or 6 done clear
  C)
             p = 2 and q = 0 or 8             done clear
  D)
             p = - 2 and q = - 2 or 8 done clear
  View Solution play_arrow

• question_answer23)
  If the equation \[A{{x}^{2}}+2Bxy+C{{y}^{2}}+Dx+Ey+F=0\] represents a pair of straight lines, then \[{{B}^{2}}-AC\] [MP PET 1992]
  A)
             < 0  done clear
  B)
             = 0 done clear
  C)
             > 0  done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer24)
  The equation of the lines passing through the origin and having slopes 3 and \[-\frac{1}{3}\] is
  A)
             \[3{{y}^{2}}+8xy-3{{x}^{2}}=0\]                                        done clear
  B)
             \[3{{x}^{2}}+8xy-3{{y}^{2}}=0\] done clear
  C)
             \[3{{y}^{2}}-8xy+3{{x}^{2}}=0\]                                        done clear
  D)
             \[3{{x}^{2}}+8xy+3{{y}^{2}}=0\] done clear
  View Solution play_arrow

• question_answer25)
  The equation \[xy+{{a}^{2}}=a(x+y)\] represents [MP PET 1991]
  A)
             A parabola                             done clear
  B)
             A pair of straight lines done clear
  C)
             An ellipse                               done clear
  D)
             Two parallel straight lines done clear
  View Solution play_arrow

• question_answer26)
  If the slope of one of the line represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] be l times that of the other, then
  A)
             \[4\lambda h=ab(1+\lambda )\]                                      done clear
  B)
             \[\lambda h=ab{{(1+\lambda )}^{2}}\] done clear
  C)
             \[4\lambda {{h}^{2}}=ab{{(1+\lambda )}^{2}}\]        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer27)
  If one of the line represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] is coincident with one of the line represented by \[{a}'{{x}^{2}}+2{h}'xy+{b}'{{y}^{2}}=0\], then
  A)
             \[{{(a{b}'-{a}'b)}^{2}}=4(a{h}'-{a}'h)\,(h{b}'-{h}'b)\] done clear
  B)
             \[{{(a{b}'+{a}'b)}^{2}}=4(a{h}'-{a}'h)\,(h{b}'-{h}'b)\] done clear
  C)
             \[{{(a{b}'-{a}'b)}^{2}}=(a{h}'-{a}'h)\,(h{b}'-{h}'b)\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer28)
  The equation \[4{{x}^{2}}+12xy+9{{y}^{2}}+2gx+2fy+c=0\] will represents two real parallel straight lines, if
  A)
             g = 4, f = 9, c = 0                   done clear
  B)
             g = 2, f = 3, c = 1 done clear
  C)
             g = 2, f = 3, c is any number done clear
  D)
             g = 4, f = 9, c > 1 done clear
  View Solution play_arrow

• question_answer29)
  The equation \[2{{y}^{2}}-xy-{{x}^{2}}+6x-8=0\] represents [MP PET 1992]
  A)
             A pair of straight lines       done clear
  B)
             A circle done clear
  C)
             An ellipse                               done clear
  D)
             A parabola done clear
  View Solution play_arrow

• question_answer30)
  One of the lines represented by the equation \[{{x}^{2}}+6xy=0\] is
  A)
             Parallel to x-axis                  done clear
  B)
             Parallel to y-axis done clear
  C)
             x-axis                                       done clear
  D)
             y-axis done clear
  View Solution play_arrow

• question_answer31)
  The equation of the lines represented by the equation \[{{x}^{2}}-5xy+6{{y}^{2}}=0\] are
  A)
             \[y+2x=0\], \[y-3x=0\]      done clear
  B)
             \[y-2x=0\], \[y-3x=0\] done clear
  C)
             \[y+2x=0\], \[y+3x=0\]     done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer32)
  If the equation \[a{{x}^{2}}+b{{y}^{2}}+cx+cy=0\] represents a pair of straight lines, then
  A)
             \[a(b+c)=0\]                          done clear
  B)
             \[b(c+a)=0\] done clear
  C)
             \[c(a+b)=0\]                          done clear
  D)
             \[a+b+c=0\] done clear
  View Solution play_arrow

• question_answer33)
  The equations of the lines represented by the equation \[a{{x}^{2}}+(a+b)xy+b{{y}^{2}}+x+y=0\] are
  A)
             \[ax+by+1=0\], \[x+y=0\] done clear
  B)
             \[ax+by-1=0\], \[x+y=0\] done clear
  C)
             \[ax+by+1=0\], \[x-y=0\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer34)
  The equation \[{{x}^{2}}-7xy+12{{y}^{2}}=0\] represents [BIT Ranchi 1991]
  A)
             Circle done clear
  B)
             Pair of parallel straight lines done clear
  C)
             Pair of perpendicular straight lines done clear
  D)
             Pair of non-perpendicular intersecting straight lines done clear
  View Solution play_arrow

• question_answer35)
  The equation \[{{y}^{2}}-{{x}^{2}}+2x-1=0\] represents [MNR 1991]
  A)
             A pair of straight lines       done clear
  B)
             A circle done clear
  C)
             A parabola                             done clear
  D)
             An ellipse done clear
  View Solution play_arrow

• question_answer36)
  If the equation \[\lambda {{x}^{2}}+2{{y}^{2}}-5xy+5x-7y+3=0\] represents two straight lines, then the value of l will be [RPET 1989]
  A)
             3     done clear
  B)
             2 done clear
  C)
             8     done clear
  D)
             - 8 done clear
  View Solution play_arrow

• question_answer37)
  The equation of one of the line represented by the equation \[{{x}^{2}}+2xy\cot \theta -{{y}^{2}}=0\], is
  A)
             \[x-y\cot \theta =0\] done clear
  B)
             \[x+y\tan \theta =0\] done clear
  C)
             \[x\sin \theta +y(\cos \theta +1)=0\] done clear
  D)
             \[x\cos \theta +y(\sin \theta +1)=0\] done clear
  View Solution play_arrow

• question_answer38)
  The equation of one of the line represented by the equation \[pq({{x}^{2}}-{{y}^{2}})+({{p}^{2}}-{{q}^{2}})xy=0\], is
  A)
             \[px+qy=0\]                          done clear
  B)
             \[px-qy=0\] done clear
  C)
             \[{{p}^{2}}x+{{q}^{2}}y=0\]    done clear
  D)
             \[{{q}^{2}}x-{{p}^{2}}y=0\] done clear
  View Solution play_arrow

• question_answer39)
  The pair of straight lines passes through the point (1, 2) and perpendicular to the pair of straight lines \[3{{x}^{2}}-8xy+5{{y}^{2}}=0\], is
  A)
             \[(5x+3y+11)(x+y+3)=0\] done clear
  B)
             \[(5x+3y-11)(x+y-3)=0\] done clear
  C)
             \[(3x+5y-11)(x+y+3)=0\] done clear
  D)
             \[(3x-5y+11)(x+y-3)=0\] done clear
  View Solution play_arrow

• question_answer40)
  If in general quadratic equation \[f(x,\,y)=0\], \[\Delta =0\] and \[{{h}^{2}}=ab\], then the equation represents
  A)
             Two parallel straight lines done clear
  B)
             Two perpendicular straight lines done clear
  C)
             Two coincident lines done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer41)
  The condition of representing the coincident lines by the general quadratic equation \[f(x,\,y)=0\], is
  A)
  \[\Delta =0\] and \[{{h}^{2}}=ab\] done clear
  B)
  \[\Delta =0\] and \[a+b=0\]   done clear
  C)
  \[\Delta =0\] and \[{{h}^{2}}=ab\], \[{{g}^{2}}=ac\], \[{{f}^{2}}=bc\] done clear
  D)
  \[{{h}^{2}}=ab\], \[{{g}^{2}}=ac\] and \[{{f}^{2}}=bc\] done clear
  View Solution play_arrow

• question_answer42)
  The equation \[{{x}^{2}}+k{{y}^{2}}+4xy=0\]represents two coincident lines, if k =                                           [MP PET 1995]
  A)
             0     done clear
  B)
             1 done clear
  C)
             4     done clear
  D)
             16 done clear
  View Solution play_arrow

• question_answer43)
  The joint equation of the straight lines \[x+y=1\]and \[x-y=4\]is                                                [Karnataka CET 1993]
  A)
             \[{{x}^{2}}-{{y}^{2}}=-4\] done clear
  B)
             \[{{x}^{2}}-{{y}^{2}}=4\] done clear
  C)
             \[(x+y-1)\,(x-y-4)=0\]       done clear
  D)
             \[(x+y+1)(x-y+4)=0\] done clear
  View Solution play_arrow

• question_answer44)
  The value of \[\lambda \] for which the equation \[{{x}^{2}}-\lambda xy+2{{y}^{2}}+3x-5y+2=0\] may represent a pair of straight lines is [Kurukshetra CEE 1996]
  A)
             2     done clear
  B)
             3 done clear
  C)
             4     done clear
  D)
             1 done clear
  View Solution play_arrow

• question_answer45)
  \[2{{x}^{2}}+7xy+3{{y}^{2}}+8x+14y+\lambda =0\] will represent a pair of straight lines, when \[\lambda \]=                                         [MP PET 1996]
  A)
             2     done clear
  B)
             4 done clear
  C)
             6     done clear
  D)
             8 done clear
  View Solution play_arrow

• question_answer46)
  The gradient  of one of the lines \[{{x}^{2}}+hxy+2{{y}^{2}}=0\] is twice that of the other, then h =                          [MP PET 1996]
  A)
             \[\pm \,3\]                            done clear
  B)
             \[\pm \,\frac{3}{2}\] done clear
  C)
             \[\pm \,2\]                            done clear
  D)
             \[\pm \,1\] done clear
  View Solution play_arrow

• question_answer47)
  If the point (2,-3) lies on \[k{{x}^{2}}-3{{y}^{2}}+2x+y-2=0\], then k is equal to
  A)
             \[\frac{1}{7}\]                       done clear
  B)
             16 done clear
  C)
             7     done clear
  D)
             12 done clear
  View Solution play_arrow

• question_answer48)
  If \[L{{x}^{2}}-10xy+12{{y}^{2}}\]\[+5x-16y-3=0\] represents a pair of straight lines, then L is                                       [MP PET 2001]
  A)
             1     done clear
  B)
             2 done clear
  C)
             3     done clear
  D)
             -1 done clear
  View Solution play_arrow

• question_answer49)
  If the ratio of gradients of the lines represented by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]is  1 : 3, then the value of the ratio \[{{h}^{2}}:ab\]is                                                        [MP PET 1998]
  A)
             \[\frac{1}{3}\]                       done clear
  B)
             \[\frac{3}{4}\] done clear
  C)
             \[\frac{4}{3}\]                       done clear
  D)
             1 done clear
  View Solution play_arrow

• question_answer50)
  If the slope of one line of the pair of lines represented by \[a{{x}^{2}}+4xy+{{y}^{2}}=0\]is 3 times the slope of the other line, then a is                                                                                                     [DCE 1999]
  A)
             1     done clear
  B)
             2 done clear
  C)
             3     done clear
  D)
             4 done clear
  View Solution play_arrow

• question_answer51)
  If the sum of slopes of the pair of lines represented by \[4{{x}^{2}}+2hxy-7{{y}^{2}}=0\]is equal to the product of the slopes, then the value of\[h\]is                                                                 [Karnataka CET 1999]
  A)
             - 6   done clear
  B)
             - 2 done clear
  C)
             - 4   done clear
  D)
             4 done clear
  View Solution play_arrow

• question_answer52)
  The gradient of one of the lines of \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] is twice that of the other, then [MP PET 2000; Pb. CET 2002]
  A)
             \[{{h}^{2}}=ab\]                  done clear
  B)
             \[h=a+b\] done clear
  C)
             \[8{{h}^{2}}=9ab\]              done clear
  D)
             \[9{{h}^{2}}=8ab\] done clear
  View Solution play_arrow

• question_answer53)
  The equation \[{{x}^{2}}+kxy+{{y}^{2}}-5x-7y+6=0\] represents a pair of straight lines, then k is                                [MP PET 2000]
  A)
             5/3 done clear
  B)
             10/3 done clear
  C)
             3/2 done clear
  D)
             3/10 done clear
  View Solution play_arrow

• question_answer54)
  The equation \[2{{x}^{2}}+4xy-k{{y}^{2}}+4x+2y-1=0\] represents a pair of lines.  The value of k is [Karnataka CET 2001]
  A)
             \[-\frac{5}{3}\]                     done clear
  B)
             \[\frac{5}{3}\] done clear
  C)
             \[\frac{1}{3}\]                       done clear
  D)
             \[-\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer55)
  Separate equations of lines, for a pair of lines, whose equation is \[{{x}^{2}}+xy-12{{y}^{2}}=0\], are [Karnataka CET 2001; Pb. CET 2000]
  A)
             \[x+4y=0\]and \[x+3y=0\] done clear
  B)
             \[2x-3y=0\] and \[x-4y=0\] done clear
  C)
             \[x-6y=0\]and \[x-3y=0\]        done clear
  D)
             \[x+4y=0\]and \[x-3y=0\] done clear
  View Solution play_arrow

• question_answer56)
  The value of k so that the equation \[2{{x}^{2}}+5xy+3{{y}^{2}}+6x+7y+k=0\] represents a pair of straight lines, is [Kurukshetra CEE 2002]
  A)
             4     done clear
  B)
             6 done clear
  C)
             0     done clear
  D)
             8 done clear
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• question_answer57)
  If the equation \[3{{x}^{2}}+xy-{{y}^{2}}-3x+6y+k=0\] represents a pair of lines, then k is equal to            [Karnataka CET 2002]
  A)
             9     done clear
  B)
             1 done clear
  C)
             0     done clear
  D)
             - 9 done clear
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• question_answer58)
  Equation  \[3{{x}^{2}}+7xy+2{{y}^{2}}+5x+5y+2=0\] represents [UPSEAT 2002]
  A)
             Pair of straight line             done clear
  B)
             Ellipse done clear
  C)
             Hyperbola                              done clear
  D)
             None of these done clear
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• question_answer59)
  For what value of \['p'\], \[{{y}^{2}}+xy+p{{x}^{2}}-x-2y=0\] represents two straight lines                                            [UPSEAT 2002]
  A)
             2     done clear
  B)
             \[\frac{1}{3}\] done clear
  C)
             \[\frac{1}{4}\]                       done clear
  D)
             \[\frac{1}{2}\] done clear
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• question_answer60)
  If the equation \[2{{x}^{2}}+7xy+3{{y}^{2}}-9x-7y+k=0\] represents a pair of lines, then k is equal to       [Kerala (Engg.) 2002]
  A)
             4     done clear
  B)
             2 done clear
  C)
             1     done clear
  D)
             - 4 done clear
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• question_answer61)
  If the equation \[12{{x}^{2}}-10xy+2{{y}^{2}}+11x-5y+k=0\] represents two straight lines, then the value  of k is [MP PET 2003]
  A)
             1     done clear
  B)
             2 done clear
  C)
             0     done clear
  D)
             3 done clear
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• question_answer62)
  If two sides of a  triangle are represented by \[{{x}^{2}}-7xy+6{{y}^{2}}=0\] and the centroid is (1, 0) then the equation of third side is
  A)
             \[2x+7y+3=0\]                      done clear
  B)
             \[2x-7y+3=0\] done clear
  C)
             \[2x+7y-3=0\]                       done clear
  D)
             \[2x-7y-3=0\] done clear
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• question_answer63)
  The equation \[4{{x}^{2}}-24xy+11{{y}^{2}}=0\]represents  [Orissa JEE 2003]
  A)
             Two parallel lines                done clear
  B)
             Two perpendicular lines done clear
  C)
             Two lines through the origin done clear
  D)
             A circle done clear
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• question_answer64)
  If the slope of one of the lines given by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]is 5 times the other, then [Karnataka CET 2003]
  A)
             \[5{{h}^{2}}=ab\]                done clear
  B)
             \[5{{h}^{2}}=9ab\] done clear
  C)
             \[9{{h}^{2}}=5ab\]              done clear
  D)
             \[{{h}^{2}}=ab\] done clear
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• question_answer65)
  The equation to the pair  of straight lines through the origin which are perpendicular to the lines \[2{{x}^{2}}-5xy+{{y}^{2}}=0,\]is [MP PET 1990]
  A)
             \[2{{x}^{2}}+5xy+{{y}^{2}}=0\]                                         done clear
  B)
             \[{{x}^{2}}+2{{y}^{2}}+5xy=0\] done clear
  C)
             \[{{x}^{2}}-5xy+2{{y}^{2}}=0\]                                          done clear
  D)
             \[2{{x}^{2}}+{{y}^{2}}-5xy=0\] done clear
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• question_answer66)
  The area of the triangle formed by the lines \[{{x}^{2}}-4{{y}^{2}}=0\]and \[x=a\], is                      
  A)
             \[2{{a}^{2}}\]                        done clear
  B)
             \[\frac{{{a}^{2}}}{2}\] done clear
  C)
             \[\frac{\sqrt{3}{{a}^{2}}}{2}\]                                            done clear
  D)
             \[\frac{2{{a}^{2}}}{\sqrt{3}}\] done clear
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• question_answer67)
  If the lines represented by the equation \[6{{x}^{2}}+41xy-7{{y}^{2}}=0\] make angles \[\alpha \]and \[\beta \] with x-axis, then \[\tan \alpha .\tan \beta \]=
  A)
             - 6/7                                          done clear
  B)
             6/ 7 done clear
  C)
             7/6 done clear
  D)
             - 7/6 done clear
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• question_answer68)
  Difference of slopes of the lines represented by equation \[{{x}^{2}}({{\sec }^{2}}\theta -{{\sin }^{2}}\theta )-2xy\tan \theta +{{y}^{2}}{{\sin }^{2}}\theta =0\]is [Kurukshetra CEE 2002]
  A)
             4     done clear
  B)
             3 done clear
  C)
             2     done clear
  D)
             None of these done clear
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• question_answer69)
  The value of \[\lambda ,\] for which the equation \[{{x}^{2}}-{{y}^{2}}-x\]?\[\lambda y-2=0\]represent a pair of straight line, are [MP PET 2004]
  A)
             3, - 3                                         done clear
  B)
             - 3, 1                                         done clear
  C)
             3, 1 done clear
  D)
             -1, 1 done clear
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• question_answer70)
  If \[a{{x}^{2}}-{{y}^{2}}+4x-y=0\]represents a pair of lines then \[a=\] [Karnataka CET  2004]
  A)
             - 16                                            done clear
  B)
             16 done clear
  C)
             4     done clear
  D)
             - 4 done clear
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• question_answer71)
  If one of the lines given by \[6{{x}^{2}}-xy+4c{{y}^{2}}=0\] is \[3x+4y=0\], then c equals                                                [AIEEE 2004]
  A)
             - 3   done clear
  B)
             - 1 done clear
  C)
             3     done clear
  D)
             1 done clear
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• question_answer72)
  If the sum of the slopes of the lines given by \[{{x}^{2}}-2cxy-7{{y}^{2}}=0\] is four times their product, then c has the value [AIEEE 2004]
  A)
             - 2   done clear
  B)
             - 1 done clear
  C)
             2     done clear
  D)
             1 done clear
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• question_answer73)
  If \[\frac{{{x}^{2}}}{a}+\frac{{{y}^{2}}}{b}+\frac{2xy}{h}=0\] represent pair of straight lines and slope of one line is twice the other. Then \[ab:{{h}^{2}}\] is [DCE 2005]
  A)
             9 : 8                                           done clear
  B)
             8 : 9 done clear
  C)
             1 : 2                                           done clear
  D)
             2 : 1 done clear
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