JEE Main & Advanced Mathematics Straight Line Question Bank

done Angle between two straight lines, Bisector of angle between two lines Total Questions - 37

• question_answer1)
  The acute angle between the lines \[y=3\] and \[y=\sqrt{3}x+9\] is [RPET 1984, 87, 88]
  A)
             \[{{30}^{o}}\]                       done clear
  B)
             \[{{60}^{o}}\] done clear
  C)
             \[{{45}^{o}}\]                       done clear
  D)
             \[{{90}^{o}}\] done clear
  View Solution play_arrow

• question_answer2)
  The angle between the lines \[y=(2-\sqrt{3})x+5\] and \[y=(2+\sqrt{3})x-7\] is                                       [MP PET 1997]
  A)
             \[{{30}^{o}}\]                       done clear
  B)
             \[{{60}^{o}}\] done clear
  C)
             \[{{45}^{o}}\]                       done clear
  D)
             \[{{90}^{o}}\] done clear
  View Solution play_arrow

• question_answer3)
  The angle between the lines whose intercepts on the axes are a, -b and b, -a respectively, is
  A)
  \[{{\tan }^{-1}}\frac{{{a}^{2}}-{{b}^{2}}}{ab}\]         done clear
  B)
  \[{{\tan }^{-1}}\frac{{{b}^{2}}-{{a}^{2}}}{2}\] done clear
  C)
  \[{{\tan }^{-1}}\frac{{{b}^{2}}-{{a}^{2}}}{2ab}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer4)
  If the coordinates of the vertices A, B, C of the triangle ABC be \[(-\ 4,\ 2),\] \[(12,\ -2)\] and \[(8,\ 6)\]respectively, then \[\angle \ B\]=
  A)
             \[{{\tan }^{-1}}\left( -\frac{6}{7} \right)\] done clear
  B)
             \[{{\tan }^{-1}}\left( \frac{6}{7} \right)\] done clear
  C)
             \[{{\tan }^{-1}}\left( -\frac{7}{6} \right)\] done clear
  D)
             \[{{\tan }^{-1}}\left( \frac{7}{6} \right)\] done clear
  View Solution play_arrow

• question_answer5)
  Angle between the lines \[\frac{x}{a}+\frac{y}{b}=1\] and \[\frac{x}{a}-\frac{y}{b}=1\] is  [MP PET 1995]
  A)
             \[2{{\tan }^{-1}}\frac{b}{a}\]     done clear
  B)
             \[{{\tan }^{-1}}\frac{2ab}{{{a}^{2}}+{{b}^{2}}}\] done clear
  C)
             \[{{\tan }^{-1}}\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]               done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer6)
  If the lines \[y=3x+1\] and \[2y=x+3\] are equally inclined to the line \[y=mx+4,\] then m =                                [ISM Dhanbad 1976]
  A)
             \[\frac{1+3\sqrt{2}}{7}\]       done clear
  B)
             \[\frac{1-3\sqrt{2}}{7}\] done clear
  C)
             \[\frac{1\pm 3\sqrt{2}}{7}\]   done clear
  D)
             \[\frac{1\pm 5\sqrt{2}}{7}\] done clear
  View Solution play_arrow

• question_answer7)
  The angle between the lines \[x\cos {{\alpha }_{1}}+y\sin {{\alpha }_{1}}={{p}_{1}}\] and \[x\cos {{\alpha }_{2}}+y\sin {{\alpha }_{2}}={{p}_{2}}\]is
  A)
             \[({{\alpha }_{1}}+{{\alpha }_{2}})\]                                    done clear
  B)
             \[({{\alpha }_{1}}\tilde{\ }{{\alpha }_{2}})\] done clear
  C)
             \[2{{\alpha }_{1}}\]                done clear
  D)
             \[2{{\alpha }_{2}}\] done clear
  View Solution play_arrow

• question_answer8)
  The angle between the lines \[x\cos {{30}^{o}}+y\sin 30{}^\circ =3\] and \[x\cos {{60}^{o}}+y\sin {{60}^{o}}=5\] is
  A)
             \[{{90}^{o}}\]                       done clear
  B)
             \[{{30}^{o}}\] done clear
  C)
             \[{{60}^{o}}\]                       done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer9)
  The angle between the two lines \[y-2x=9\] and \[x+2y=-\ 7,\] is             [RPET 1981, 85, 86; MP PET 1984]
  A)
             \[{{60}^{o}}\]                       done clear
  B)
             \[{{30}^{o}}\] done clear
  C)
             \[{{90}^{o}}\]                       done clear
  D)
             \[{{45}^{o}}\] done clear
  View Solution play_arrow

• question_answer10)
  If \[\frac{1}{a{b}'}+\frac{1}{b{a}'}=0,\] then lines \[\frac{x}{a}+\frac{y}{b}=1\] and \[\frac{x}{{{b}'}}+\frac{y}{{{a}'}}=1\] are  [MP PET 1984]
  A)
  Parallel      done clear
  B)
  Inclined at \[{{60}^{o}}\]to each other done clear
  C)
  Perpendicular to each other               done clear
  D)
  Inclined at \[{{30}^{o}}\]to each other done clear
  View Solution play_arrow

• question_answer11)
  To which of the following types the straight lines represented by \[2x+3y-7=0\] and \[2x+3y-5=0\] belong  [MP PET 1982]
  A)
  Parallel to each other                          done clear
  B)
  Perpendicular to each other done clear
  C)
  Inclined at \[{{45}^{o}}\]to each other                                             done clear
  D)
  Coincident pair of straight lines done clear
  View Solution play_arrow

• question_answer12)
  The obtuse angle between the lines \[y=-\ 2\] and \[y=x+2\] is                                                     [RPET 1984]
  A)
             \[{{120}^{o}}\]                     done clear
  B)
             \[{{135}^{o}}\] done clear
  C)
             \[{{150}^{o}}\]                     done clear
  D)
             \[{{160}^{o}}\] done clear
  View Solution play_arrow

• question_answer13)
  The line passes through (1, 0) and \[(-\ 2,\ \sqrt{3})\] makes an angle of ...... with x?axis                                           [RPET 1985]
  A)
             \[{{60}^{o}}\]                       done clear
  B)
             \[{{120}^{o}}\] done clear
  C)
             \[{{150}^{o}}\]                     done clear
  D)
             \[{{135}^{o}}\] done clear
  View Solution play_arrow

• question_answer14)
  Angle between \[x=2\] and \[x-3y=6\] is                      [MNR 1988]
  A)
             \[\infty \]                                     done clear
  B)
             \[{{\tan }^{-1}}(3)\] done clear
  C)
             \[{{\tan }^{-1}}\left( \frac{1}{3} \right)\]                                done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer15)
  If the lines \[y=(2+\sqrt{3})x+4\] and \[y=kx+6\]are inclined at an angle \[{{60}^{o}}\]to each other, then the value of k will be
  A)
  1         done clear
  B)
  2 done clear
  C)
  1         done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer16)
  A straight line \[(\sqrt{3}-1)x=(\sqrt{3}+1)y\] makes an angle \[{{75}^{o}}\]with another straight line which passes through origin. Then the equation of the line is
  A)
             \[x=0\]                                       done clear
  B)
             \[y=0\] done clear
  C)
             \[x+y=0\]                                 done clear
  D)
             \[x-y=0\] done clear
  View Solution play_arrow

• question_answer17)
  The angle between the lines \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0,\] is                                             [MP PET 1994]
  A)
             \[{{\tan }^{-1}}\frac{{{a}_{1}}{{b}_{2}}+{{a}_{2}}{{b}_{1}}}{{{a}_{1}}{{a}_{2}}-{{b}_{1}}{{b}_{2}}}\]             done clear
  B)
             \[{{\cot }^{-1}}\frac{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}{{{a}_{1}}{{b}_{2}}-{{a}_{2}}{{b}_{1}}}\] done clear
  C)
             \[{{\cot }^{-1}}\frac{{{a}_{1}}{{b}_{1}}-{{a}_{2}}{{b}_{2}}}{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}\]              done clear
  D)
             \[{{\tan }^{-1}}\frac{{{a}_{1}}{{b}_{1}}-{{a}_{2}}{{b}_{2}}}{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}\] done clear
  View Solution play_arrow

• question_answer18)
  The inclination of the straight line passing through the point (-3, 6) and the midpoint of the line joining the point (4, -5) and (-2, 9) is  [Kerala (Engg.) 2002]
  A)
  \[\pi /4\]                                      done clear
  B)
  \[\pi /6\] done clear
  C)
  \[\pi /3\]                                      done clear
  D)
  \[3\pi /4\] done clear
  View Solution play_arrow

• question_answer19)
  The angle between the lines \[2x-y+3=0\] and \[x+2y+3=0\] is                                 [Kerala (Engg.) 2002]
  A)
             \[{{90}^{o}}\]                       done clear
  B)
             \[{{60}^{o}}\] done clear
  C)
             \[{{45}^{o}}\]                       done clear
  D)
             \[{{30}^{o}}\] done clear
  View Solution play_arrow

• question_answer20)
  The angle between the straight lines \[x-y\sqrt{3}=5\] and \[\sqrt{3x}+y=7\]is                                          [MP PET 2003]
  A)
             \[{{90}^{o}}\]                       done clear
  B)
             \[{{60}^{o}}\] done clear
  C)
             \[{{75}^{o}}\]                       done clear
  D)
             \[{{30}^{o}}\] done clear
  View Solution play_arrow

• question_answer21)
  Angle between the lines \[2x-y-15=0\] and \[3x+y+4=0\]is                                         [RPET 2003]
  A)
             \[{{90}^{o}}\]                       done clear
  B)
             \[{{45}^{o}}\] done clear
  C)
             \[{{180}^{o}}\]                     done clear
  D)
             \[{{60}^{o}}\] done clear
  View Solution play_arrow

• question_answer22)
  The angle between the lines \[xy=0\]is equal to [Pb. CET 2003]
  A)
             \[{{45}^{o}}\]                       done clear
  B)
             \[60{}^\circ \] done clear
  C)
             \[{{90}^{o}}\] done clear
  D)
             \[{{180}^{o}}\] done clear
  View Solution play_arrow

• question_answer23)
  The line passing through the points (3, -4) and   (-2, 6) and a line passing through (-3,6) and (9, -18) are         [AMU 1974]
  A)
  Perpendicular                                      done clear
  B)
  Parallel done clear
  C)
  Makes an angle \[{{60}^{o}}\]with each other done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer24)
  If the line \[2x+3ay-1=0\] and \[3x+4y+1=0\] are mutually perpendicular, then the value of a will be                 [MNR 1975]
  A)
             \[\frac{1}{2}\]                           done clear
  B)
  2 done clear
  C)
             \[-\frac{1}{2}\]                         done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer25)
  A straight line through origin bisect the line passing through the given points \[(a\cos \alpha ,a\sin \alpha )\]and \[(a\cos \beta ,a\sin \beta )\], then the lines are
  A)
  Perpendicular                                      done clear
  B)
  Parallel done clear
  C)
  Angle between them is \[\frac{\pi }{4}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer26)
  The lines \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] are perpendicular to each other, if                        [MP PET 1996]
  A)
             \[{{a}_{1}}{{b}_{2}}-{{b}_{1}}{{a}_{2}}=0\]                 done clear
  B)
             \[{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}=0\] done clear
  C)
             \[a_{1}^{2}{{b}_{2}}+b_{1}^{2}{{a}_{2}}=0\]          done clear
  D)
             \[{{a}_{1}}{{b}_{1}}+{{a}_{2}}{{b}_{2}}=0\] done clear
  View Solution play_arrow

• question_answer27)
  The lines \[y=2x\]and \[x=-2y\]are          [MP PET 1993]
  A)
  Parallel      done clear
  B)
  Perpendicular done clear
  C)
  Equally inclined to axes                      done clear
  D)
  Coincident done clear
  View Solution play_arrow

• question_answer28)
  If the line passing through (4, 3) and (2, k) is perpendicular to \[y=2x+3\], then k =                    [RPET 1985; MP PET 1999]
  A)
  -1        done clear
  B)
  1 done clear
  C)
  4         done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer29)
  The number of straight lines which is equally inclined to both the axes is                                       [RPET 2002]
  A)
  4         done clear
  B)
  2 done clear
  C)
  3         done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer30)
  The equation of the bisector of the acute angle between the lines \[3x-4y+7=0\]and \[12x+5y-2=0\]is [IIT 1975, 1983; RPET 2003; UPSEAT 2004]
  A)
             \[21x+77y-101=0\]                done clear
  B)
             \[11x-3y+9=0\] done clear
  C)
             \[31x+77y+101=0\]              done clear
  D)
             \[11x-3y-9=0\] done clear
  View Solution play_arrow

• question_answer31)
  The equation of the line which bisects the obtuse angle between the lines \[x-2y+4=0\] and \[4x-3y+2=0\], is  [IIT 1979]
  A)
             \[(4-\sqrt{5})x-(3-2\sqrt{5})y+(2-4\sqrt{5})=0\] done clear
  B)
             \[(4+\sqrt{5})x-(3+2\sqrt{5})y+(2+4\sqrt{5})=0\] done clear
  C)
             \[(4+\sqrt{5})x+(3+2\sqrt{5})y+(2+4\sqrt{5})=0\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer32)
  Equation of angle bisectors between x and y -axes are [MP PET 1984]
  A)
             \[y=\pm x\]                               done clear
  B)
             \[y=\pm 2x\] done clear
  C)
             \[y=\pm \frac{1}{\sqrt{2}}x\]        done clear
  D)
   \[y=\pm 3x\] done clear
  View Solution play_arrow

• question_answer33)
  The equation of the bisector of that angle between the lines \[x+2y-11=0\], \[3x-6y-5=0\]which contains the point (1, ?3) is
  A)
             \[3x=19\]                                  done clear
  B)
             \[3y=7\] done clear
  C)
             \[3x=19\]and \[3y=7\]            done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer34)
  Equation of angle bisector between the lines \[3x+4y-7=0\] and \[12x+5y+17=0\]are           [RPET 1995]
  A)
             \[\frac{3x+4y-7}{\sqrt{25}}=\pm \frac{12x+5y+17}{\sqrt{169}}\] done clear
  B)
             \[\frac{3x+4y+7}{\sqrt{25}}=\frac{12x+5y+17}{\sqrt{169}}\] done clear
  C)
             \[\frac{3x+4y+7}{\sqrt{25}}=\pm \frac{12x+5y+17}{\sqrt{169}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer35)
  The bisector of the acute angle formed between the lines \[4x-3y+7=0\]and \[3x-4y+14=0\]has the equation  [Pb. CET 2004]
  A)
             \[x+y+3=0\]                            done clear
  B)
             \[x-y-3=0\] done clear
  C)
             \[x-y+3=0\]                              done clear
  D)
             \[3x+y-7=0\] done clear
  View Solution play_arrow

• question_answer36)
  If vertices of a parallelogram are respectively (0, 0), (1, 0), (2, 2) and (1, 2), then angle between diagonals is  [RPET 1996]
  A)
             \[\pi /3\]                                      done clear
  B)
             \[\pi /2\] done clear
  C)
             \[3\pi /2\]                                   done clear
  D)
             \[\pi /4\] done clear
  View Solution play_arrow

• question_answer37)
  Let \[P(-1,\,0),\,\] \[Q(0,\,0)\] and \[R\,(3,\,3\sqrt{3})\] be three points. Then the equation of the bisector of the angle PQR is  [IIT Screening 2002]
  A)
             \[\frac{\sqrt{3}}{2}x+y=0\]  done clear
  B)
             \[x+\sqrt{3}y=0\] done clear
  C)
             \[\sqrt{3}x+y=0\]                    done clear
  D)
             \[x+\frac{\sqrt{3}}{2}y=0\] done clear
  View Solution play_arrow