JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank

done Bisectors of the angle between the lines, Point of intersection of the lines Total Questions - 16

• question_answer1)
  The line \[x-2y=0\]will be a bisector of the angle between the lines represented by the equation \[{{x}^{2}}-2hxy-2{{y}^{2}}=0\], if \[h=\]              
  A)
             1/2 done clear
  B)
             2 done clear
  C)
   \[-2\]       done clear
  D)
             -1/2 done clear
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• question_answer2)
  The equation of the bisectors of the angle between lines represented by equation \[4{{x}^{2}}-16xy-7{{y}^{2}}=0\]is
  A)
             \[8{{x}^{2}}+11xy-8{{y}^{2}}=0\]                                     done clear
  B)
             \[8{{x}^{2}}-11xy-8{{y}^{2}}=0\] done clear
  C)
             \[16{{x}^{2}}+11xy-16{{y}^{2}}=0\]                                 done clear
  D)
             \[16{{x}^{2}}+11xy+16{{y}^{2}}=0\] done clear
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• question_answer3)
  The equation of the bisectors of angle between the lines represented by equation \[{{(y-mx)}^{2}}={{(x+my)}^{2}}\]is
  A)
             \[m{{x}^{2}}+({{m}^{2}}-1)xy-m{{y}^{2}}=0\]            done clear
  B)
             \[m{{x}^{2}}-({{m}^{2}}-1)xy-m{{y}^{2}}=0\] done clear
  C)
             \[m{{x}^{2}}+({{m}^{2}}-1)xy+m{{y}^{2}}=0\]           done clear
  D)
             None of these done clear
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• question_answer4)
  The equation of the bisectors of the angle between the lines represented by the equation \[{{x}^{2}}-{{y}^{2}}=0\], is
  A)
             \[x=0\]                                    done clear
  B)
             \[y=0\] done clear
  C)
             \[xy=0\]                                  done clear
  D)
             None of these done clear
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• question_answer5)
  If \[y=mx\]be one of the bisectors of the angle between the lines \[a{{x}^{2}}-2hxy+b{{y}^{2}}=0\], then
  A)
             \[h\,(1+{{m}^{2}})+m(a-b)=0\] done clear
  B)
             \[h\,(1-{{m}^{2}})+m(a+b)=0\] done clear
  C)
             \[h\,(1-{{m}^{2}})+m(a-b)=0\] done clear
  D)
             \[h\,(1+{{m}^{2}})+m(a+b)=0\] done clear
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• question_answer6)
  The combined equation of bisectors of angles between coordinate axes, is
  A)
             \[{{x}^{2}}+{{y}^{2}}=0\] done clear
  B)
             \[{{x}^{2}}-{{y}^{2}}=0\] done clear
  C)
             \[xy=0\]                                  done clear
  D)
             \[x+y=0\] done clear
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• question_answer7)
  If the bisectors of the angles between the pairs of lines given by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] and \[a{{x}^{2}}+2hxy+b{{y}^{2}}+\lambda ({{x}^{2}}+{{y}^{2}})=0\] be coincident, then \[\lambda =\]
  A)
             a     done clear
  B)
             b done clear
  C)
             \[h\]                                         done clear
  D)
             Any real number done clear
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• question_answer8)
  The combined equation of the bisectors of the angle between the lines represented by \[({{x}^{2}}+{{y}^{2}})\sqrt{3}=\] \[4xy\] is [MP PET 1992]
  A)
             \[{{y}^{2}}-{{x}^{2}}=0\]  done clear
  B)
             \[xy=0\] done clear
  C)
             \[{{x}^{2}}+{{y}^{2}}=2xy\]    done clear
  D)
             \[\frac{{{x}^{2}}-{{y}^{2}}}{\sqrt{3}}=\frac{xy}{2}\] done clear
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• question_answer9)
  The equation of the bisectors of the angles between the lines represented by \[{{x}^{2}}+2xy\cot \theta +{{y}^{2}}=0\], is
  A)
             \[{{x}^{2}}-{{y}^{2}}=0\]  done clear
  B)
             \[{{x}^{2}}-{{y}^{2}}=xy\] done clear
  C)
             \[({{x}^{2}}-{{y}^{2}})\cot \theta =2xy\]                       done clear
  D)
             None of these done clear
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• question_answer10)
  If the bisectors of angles represented by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] and \[a'{{x}^{2}}+2h'xy+b'{{y}^{2}}=0\] are same, then
  A)
             \[(a-b)h'=(a'-b')h\]            done clear
  B)
             \[(a-b)h=(a'-b')h'\] done clear
  C)
             \[(a+b)h'=(a'-b')h\]            done clear
  D)
             \[(a-b)h'=(a'+b')h\] done clear
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• question_answer11)
  If  \[r(1-{{m}^{2}})+m(p-q)=0\], then a bisector of the angle between the lines represented by the equation \[p{{x}^{2}}-2rxy+q{{y}^{2}}=0\], is
  A)
             \[y=x\]                                    done clear
  B)
             \[y=-x\] done clear
  C)
             \[y=mx\]                                done clear
  D)
             \[my=x\] done clear
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• question_answer12)
  If the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]has the one line as the bisector of angle between the coordinate axes, then [Bihar CEE 1990]
  A)
             \[{{(a-b)}^{2}}={{h}^{2}}\]      done clear
  B)
             \[{{(a+b)}^{2}}={{h}^{2}}\] done clear
  C)
             \[{{(a-b)}^{2}}=4{{h}^{2}}\]    done clear
  D)
             \[{{(a+b)}^{2}}=4{{h}^{2}}\] done clear
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• question_answer13)
  If the bisectors of the angles of the lines represented by \[3{{x}^{2}}-4xy+5{{y}^{2}}=0\] and \[5{{x}^{2}}+4xy+3{{y}^{2}}=0\] are same, then the angle made by the lines represented by first with the second, is
  A)
             \[{{30}^{o}}\]                        done clear
  B)
             \[{{60}^{o}}\] done clear
  C)
             \[{{45}^{o}}\]                        done clear
  D)
             \[{{90}^{o}}\] done clear
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• question_answer14)
  One bisector of the angle between the lines given by \[a{{(x-1)}^{2}}+2h\,(x-1)y+b{{y}^{2}}=0\] is \[2x+y-2=0\]. The other bisector is
  A)
             \[x-2y+1=0\]                         done clear
  B)
             \[2x+y-1=0\] done clear
  C)
             \[x+2y-1=0\]                         done clear
  D)
             \[x-2y-1=0\] done clear
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• question_answer15)
  The point of intersection of the lines represented by the equation \[2{{x}^{2}}+3{{y}^{2}}+7xy+8x+14y+8=0\] is
  A)
             (0, 2)                                         done clear
  B)
             (1, 2) done clear
  C)
             (-2, 0)                                       done clear
  D)
             (-2, 1) done clear
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• question_answer16)
  The point of intersection of the lines represented by equation \[2{{(x+2)}^{2}}+3(x+2)(y-2)-2{{(y-2)}^{2}}=0\] is
  A)
             (2, 2)                                         done clear
  B)
             (-2, -2) done clear
  C)
             (- 2, 2)                                      done clear
  D)
             (2, -2) done clear
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