JEE Main & Advanced Mathematics Straight Line Question Bank

done Distance between two lines, Perpendicular distance of the line from a point Position of point w.r.t. line Total Questions - 36

• question_answer1)
  The points on the x-axis whose perpendicular distance from the line \[\frac{x}{a}+\frac{y}{b}=1\] is a, are            [RPET 2001; MP PET 2003]
  A)
             \[\left[ \frac{a}{b}(b\pm \sqrt{{{a}^{2}}+{{b}^{2}}}),\,0 \right]\]                done clear
  B)
             \[\left[ \frac{b}{a}(b\pm \sqrt{{{a}^{2}}+{{b}^{2}}}),\,0 \right]\] done clear
  C)
             \[\left[ \frac{a}{b}(a\pm \sqrt{{{a}^{2}}+{{b}^{2}}}),\,0 \right]\]                done clear
  D)
             None of these done clear
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• question_answer2)
  The length of the perpendicular from the point \[(b,a)\]to the line \[\frac{x}{a}-\frac{y}{b}=1\], is         
  A)
             \[\left| \frac{{{a}^{2}}-ab+{{b}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|\]   done clear
  B)
             \[\left| \frac{{{b}^{2}}-ab-{{a}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|\] done clear
  C)
             \[\left| \frac{{{a}^{2}}+ab-{{b}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|\]   done clear
  D)
             None of these done clear
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• question_answer3)
  The distance between the lines \[3x+4y=9\]and \[6x+8y=15\]is   [MNR 1982; RPET 1995; MP PET 2002]
  A)
             3/2  done clear
  B)
             3/10 done clear
  C)
             6     done clear
  D)
             None of these done clear
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• question_answer4)
  The distance of the point of intersection of the lines \[2x-3y+5=0\] and \[3x+4y=0\]from the line \[5x-2y=0\] is
  A)
             \[\frac{130}{17\sqrt{29}}\] done clear
  B)
             \[\frac{13}{7\sqrt{29}}\] done clear
  C)
             \[\frac{130}{17}\]                    done clear
  D)
             None of these done clear
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• question_answer5)
  The point on the line \[x+y=4\]which lie at a unit distance from the line \[4x+3y=10\], are                     [IIT 1976]
  A)
             \[(3,\,1),(-7,\,11)\]                     done clear
  B)
             \[(3,\,1),(7,\,11)\] done clear
  C)
             \[(-3,\,1),(-7,\,11)\]                    done clear
  D)
             \[(1,\,3),(-7,\,11)\] done clear
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• question_answer6)
  If the length of the perpendicular drawn from the origin to the line whose intercepts on the axes are a and b be p, then  [Karnataka CET 2003]
  A)
             \[{{a}^{2}}+{{b}^{2}}={{p}^{2}}\]                              done clear
  B)
             \[{{a}^{2}}+{{b}^{2}}=\frac{1}{{{p}^{2}}}\] done clear
  C)
             \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{2}{{{p}^{2}}}\]        done clear
  D)
             \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{p}^{2}}}\] done clear
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• question_answer7)
  The length of perpendicular drawn from origin on the line joining \[({x}',{y}')\] and \[({x}'',{y}'')\], is
  A)
             \[\frac{x'y''+x''y'}{\sqrt{{{(x''-x')}^{2}}+{{(y''-y')}^{2}}}}\]          done clear
  B)
             \[\frac{x'y''-x''y'}{\sqrt{{{(x''-x')}^{2}}+{{(y''-y')}^{2}}}}\] done clear
  C)
             \[\frac{x'x''+y'y''}{\sqrt{{{(x''+x')}^{2}}+{{(y''+y')}^{2}}}}\]      done clear
  D)
             \[\frac{x'x''+y'y''}{\sqrt{{{(x''-x')}^{2}}+{{(y''-y')}^{2}}}}\] done clear
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• question_answer8)
  If p and \[p'\]be the distances of origin from the lines \[x\sec \alpha +y\text{cosec }\alpha =k\] and \[x\cos \alpha -y\sin \alpha =k\cos 2\alpha \], then \[4{{p}^{2}}+{{{p}'}^{2}}\]= 
  A)
             k      done clear
  B)
             \[2k\] done clear
  C)
             \[{{k}^{2}}\]                          done clear
  D)
             \[2{{k}^{2}}\] done clear
  View Solution play_arrow

• question_answer9)
  The perpendicular distance of the straight line \[12x+5y=7\] from the origin is given by                                           [MP PET 1993]
  A)
             \[\frac{7}{13}\]                        done clear
  B)
             \[\frac{12}{13}\] done clear
  C)
             \[\frac{5}{13}\]                        done clear
  D)
             \[\frac{1}{13}\] done clear
  View Solution play_arrow

• question_answer10)
  The length of perpendicular from (3, 1) on line \[4x+3y+20=0\], is                  [RPET 1989; MP PET 1984]
  A)
             6     done clear
  B)
             7 done clear
  C)
             5     done clear
  D)
             8 done clear
  View Solution play_arrow

• question_answer11)
  The distance between two parallel lines \[3x+4y-8=0\]and \[3x+4y-3=0\], is given by                            [MP PET 1984]
  A)
             4     done clear
  B)
             5 done clear
  C)
             3     done clear
  D)
             1 done clear
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• question_answer12)
  The distance between \[4x+3y=11\] and \[8x+6y=15\], is    [AMU 1979; MNR 1987; UPSEAT 2000]
  A)
             \[\frac{7}{2}\]                           done clear
  B)
             4 done clear
  C)
             \[\frac{7}{10}\]                        done clear
  D)
             None of these done clear
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• question_answer13)
  The vertex of an equilateral triangle is (2,-1) and the equation of its base in\[x+2y=1\]. The length of its sides is    [UPSEAT 2003]
  A)
             \[4/\sqrt{15}\] done clear
  B)
             \[2/\sqrt{15}\] done clear
  C)
             \[4/3\sqrt{3}\]                           done clear
  D)
             \[1/\sqrt{5}\] done clear
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• question_answer14)
  The product of the perpendiculars drawn from the points \[(\pm \sqrt{{{a}^{2}}-{{b}^{2}},}0)\] on the line\[\frac{x}{a}\cos \theta +\frac{y}{b}\sin \theta =1\], is
  A)
             \[{{a}^{2}}\]                          done clear
  B)
             \[{{b}^{2}}\] done clear
  C)
             \[{{a}^{2}}+{{b}^{2}}\] done clear
  D)
             \[{{a}^{2}}-{{b}^{2}}\] done clear
  View Solution play_arrow

• question_answer15)
  The ratio in which the line \[3x+4y+2=0\] divides the distance between \[3x+4y+5=0\] and \[3x+4y-5=0\], is
  A)
             \[7:3\]                                        done clear
  B)
             3 : 7 done clear
  C)
             \[2:3\]                                        done clear
  D)
             None of these done clear
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• question_answer16)
  If \[2p\] is the length of perpendicular from the origin to the lines \[\frac{x}{a}+\frac{y}{b}=1\], then \[{{a}^{2}},8{{p}^{2}},{{b}^{2}}\]are in
  A)
             A. P.                                            done clear
  B)
             G.P. done clear
  C)
             H. P. done clear
  D)
             None of these done clear
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• question_answer17)
  The length of the perpendicular drawn from origin upon the straight line \[\frac{x}{3}-\frac{y}{4}=1\]is                                         [MP PET 1997]
  A)
             \[2\frac{2}{5}\]                          done clear
  B)
             \[3\frac{1}{5}\] done clear
  C)
             \[4\frac{2}{5}\]                          done clear
  D)
             \[3\frac{2}{5}\] done clear
  View Solution play_arrow

• question_answer18)
  The distance between the lines \[3x-2y=1\]and \[6x+9=4y\] is                                                           [MP PET 1998]
  A)
             \[\frac{1}{\sqrt{52}}\]               done clear
  B)
             \[\frac{11}{\sqrt{52}}\] done clear
  C)
             \[\frac{4}{\sqrt{13}}\]               done clear
  D)
             \[\frac{6}{\sqrt{13}}\] done clear
  View Solution play_arrow

• question_answer19)
  Two points A and B have coordinates (1, 1) and (3, -2) respectively. The co-ordinates of a point distant \[\sqrt{85}\]from B on the line through B perpendicular to AB are                        [AMU 2000]
  A)
  (4, 7)                                          done clear
  B)
  (7, 4) done clear
  C)
  (5, 7)                                          done clear
  D)
  (-5, -3) done clear
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• question_answer20)
  The distance of the point (-2, 3) from the line \[x-y=5\]is [MP PET 2001]
  A)
             \[5\sqrt{2}\]                              done clear
  B)
             \[2\sqrt{5}\] done clear
  C)
             \[3\sqrt{5}\]                              done clear
  D)
             \[5\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer21)
  The distance of the lines \[2x-3y=4\]from the point (1, 1) measured parallel to the line \[x+y=1\] is               [Orissa JEE 2002]
  A)
             \[\sqrt{2}\]                                done clear
  B)
             \[\frac{5}{\sqrt{2}}\] done clear
  C)
             \[\frac{1}{\sqrt{2}}\]                 done clear
  D)
             6 done clear
  View Solution play_arrow

• question_answer22)
  Distance between the lines \[5x+3y-7=0\] and \[15x+9y+14=0\] is                                     [Kerala (Engg.) 2002]
  A)
             \[\frac{35}{\sqrt{34}}\]             done clear
  B)
             \[\frac{1}{3\sqrt{34}}\] done clear
  C)
             \[\frac{35}{3\sqrt{34}}\]           done clear
  D)
             \[\frac{35}{2\sqrt{34}}\] done clear
  View Solution play_arrow

• question_answer23)
  Distance between the parallel lines \[3x+4y+7=0\] and \[3x+4y-5=0\] is                                            [RPET 2003]
  A)
             \[\frac{2}{5}\]                            done clear
  B)
             \[\frac{12}{5}\] done clear
  C)
             \[\frac{5}{12}\]                          done clear
  D)
             \[\frac{3}{5}\] done clear
  View Solution play_arrow

• question_answer24)
  The position of the point (8,-9) with respect to the lines \[2x+3y-4=0\] and \[6x+9y+8=0\] is
  A)
             Point lies on the same side of the lines done clear
  B)
             Point lies on the different sides of the line done clear
  C)
             Point lies on one of the line done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer25)
  The length of perpendicular from the point \[(a\cos \alpha ,a\sin \alpha )\] upon the straight line \[y=x\tan \alpha +c,\] \[c>0\] is [MP PET 2004]
  A)
             \[c\cos \alpha \]                        done clear
  B)
             \[c{{\sin }^{2}}\alpha \] done clear
  C)
             \[c{{\sec }^{2}}\alpha \]            done clear
  D)
             \[c{{\cos }^{2}}\alpha \] done clear
  View Solution play_arrow

• question_answer26)
  The distance of point (-2, 3) from the line \[x-y=5\]is [Pb. CET 2001]
  A)
  \[5\sqrt{2}\]                              done clear
  B)
  \[2\sqrt{5}\] done clear
  C)
  \[3\sqrt{5}\]                              done clear
  D)
  \[5\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer27)
  Distance between the two parallel lines \[y=2x+7\]and \[y=2x+5\] is                                 [Orissa JEE 2004]
  A)
             \[\frac{\sqrt{5}}{2}\]                 done clear
  B)
             \[\frac{2}{5}\] done clear
  C)
             \[\frac{2}{\sqrt{5}}\]                 done clear
  D)
             \[\frac{1}{\sqrt{5}}\] done clear
  View Solution play_arrow

• question_answer28)
  In what ratio the line \[y-x+2=0\]divides the line joining the points (3, -1) and (8, 9)                                        [Karnataka CET 2002]
  A)
  1 : 2 done clear
  B)
  2 : 1 done clear
  C)
  2 : 3 done clear
  D)
  3 : 4 done clear
  View Solution play_arrow

• question_answer29)
  The perpendicular distance of the straight line \[12x+5y=7\]from the origin is equal to   [Pb. CET 2002]
  A)
             \[\frac{7}{13}\]                          done clear
  B)
             \[\frac{12}{13}\] done clear
  C)
             \[\frac{5}{13}\]                          done clear
  D)
             \[\frac{1}{13}\] done clear
  View Solution play_arrow

• question_answer30)
  A point equidistant from the lines \[4x+3y+10=0\], \[5x-12y+26=0\] and \[7x+24y-50=0\] is  [EAMCET 1994]
  A)
             \[(1,\,-1)\]                                 done clear
  B)
             \[(1,\,1)\] done clear
  C)
             \[(0,0)\]                                     done clear
  D)
             \[(0,\,1)\] done clear
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• question_answer31)
  The equation of the base of an equilateral triangle is \[x+y=2\] and the vertex is (2, -1). The length of the side of the triangle is [IIT 1973, 83, MP PET 1995; RPET 1999, 2000]
  A)
  \[\sqrt{3/2}\]                             done clear
  B)
  \[\sqrt{2}\] done clear
  C)
  \[\sqrt{2/3}\]                             done clear
  D)
  None of these done clear
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• question_answer32)
  \[(\sin \theta ,\cos \theta )\] and \[(3,\,2)\] lies on the same side of the line \[x+y=1\],  then \[\theta \] lies between                                [DCE 2005]
  A)
             \[(0,\,\,\pi /2)\]                         done clear
  B)
             \[(0,\,\pi )\] done clear
  C)
             \[(\pi /4,\pi /2)\]                       done clear
  D)
             \[(0,\,\,\pi /4)\] done clear
  View Solution play_arrow

• question_answer33)
  Which pair of points lie on the same side of \[3x-8y-7=0\] [Roorkee 1990]
  A)
             (0, -1) and (0, 0)                        done clear
  B)
             (4, -3) and (0, 1) done clear
  C)
             (-3, -4) and (1, 2)                       done clear
  D)
             (-1, -1) and (3, 7) done clear
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• question_answer34)
  Let \[\alpha \] be the distance between the lines \[-x+y=2\] and \[x-y=2\], and \[\beta \] be the distance between the lines \[4x-3y=5\] and \[6y-8x=1\], then    [J & K 2005]
  A)
             \[20\sqrt{2}\beta =11\alpha \] done clear
  B)
             \[20\sqrt{2}\alpha =11\beta \] done clear
  C)
             \[11\sqrt{2}\beta =20\alpha \] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer35)
  Choose the correct statement which describe the position of the point (?6, 2) relative to straight lines \[2x+3y-4=0\] and \[6x+9y+8=0\]                              [MP PET 1983]
  A)
             Below both the lines                 done clear
  B)
             Above both the lines done clear
  C)
             In between the lines                  done clear
  D)
             None of these done clear
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• question_answer36)
  The position  of the points (3, 4) and (2, ?6) with respect to the line \[3x-4y=8\] are       [Roorkee 1972; MP PET 1984]
  A)
             On the same side of the line done clear
  B)
             On different side of the line done clear
  C)
             One point on the line and the other outside the line done clear
  D)
             Both point on the line done clear
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