JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank

done Equation of lines joining the origin to the point of intersection of a curve and a line and Distance between the pair of lines Total Questions - 18

• question_answer1)
  The lines joining the origin to the points of intersection of the curves \[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx=0\] and \[a'{{x}^{2}}+2h'xy+b'{{y}^{2}}+2g'x=0\] will be mutually perpendicular, if                                            [UPSEAT 1999]
  A)
             \[g(a'-b')=g'(a+b)\]            done clear
  B)
             \[g(a'+b')=g'(a+b)\] done clear
  C)
             \[g(a'+b')=g'(a-b)\]            done clear
  D)
             \[g(a'-b')=g'(a-b)\] done clear
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• question_answer2)
  Distance between the lines represented by the equation \[{{x}^{2}}+2\sqrt{3}xy+3{{y}^{2}}-3x-3\sqrt{3}y-4=0\]is                    [Roorkee 1989]
  A)
             5/2 done clear
  B)
             5/4 done clear
  C)
             5     done clear
  D)
             0 done clear
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• question_answer3)
  If the lines joining origin to the points of intersection of the line \[fx-gy=\lambda \] and the curve \[{{x}^{2}}+hxy-{{y}^{2}}+gx+fy=0\] be mutually perpendicular, then
  A)
             \[\lambda =h\]                    done clear
  B)
             \[\lambda =g\] done clear
  C)
             \[\lambda =fg\]                   done clear
  D)
             \[\lambda \]may have any value done clear
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• question_answer4)
  The equation of the line joining origin to the points of intersection of the curve \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] and \[{{x}^{2}}+{{y}^{2}}-ax-ay=0\] is   
  A)
             \[{{x}^{2}}-{{y}^{2}}=0\]  done clear
  B)
             \[xy=0\] done clear
  C)
             \[xy-{{x}^{2}}=0\]               done clear
  D)
             \[{{y}^{2}}+xy=0\] done clear
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• question_answer5)
  The equation of second degree \[{{x}^{2}}+2\sqrt{2}xy+2{{y}^{2}}+4x+4\sqrt{2}y+1=0\] represents a pair of straight lines. The distance between them is  [MNR 1984; UPSEAT 2000]
  A)
             4     done clear
  B)
             \[4/\sqrt{3}\] done clear
  C)
             2     done clear
  D)
             \[2\sqrt{3}\] done clear
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• question_answer6)
  The equation of pair of straight lines joining the point of intersection of the curve \[{{x}^{2}}+{{y}^{2}}=4\] and \[y-x=2\] to the origin, is
  A)
             \[{{x}^{2}}+{{y}^{2}}={{(y-x)}^{2}}\]                               done clear
  B)
             \[{{x}^{2}}+{{y}^{2}}+{{(y-x)}^{2}}=0\] done clear
  C)
             \[{{x}^{2}}+{{y}^{2}}=4{{(y-x)}^{2}}\]                            done clear
  D)
             \[{{x}^{2}}+{{y}^{2}}+4{{(y-x)}^{2}}=0\] done clear
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• question_answer7)
  The lines joining the points of intersection of line \[x+y=1\] and curve \[{{x}^{2}}+{{y}^{2}}-2y+\lambda =0\]  to the origin are perpendicular, then the value of \[1/\sqrt{10}\] will be
  A)
             1/2 done clear
  B)
             -1/2 done clear
  C)
             \[1/\sqrt{2}\]                        done clear
  D)
             0 done clear
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• question_answer8)
  The lines joining the points of intersection of curve \[5{{x}^{2}}+12xy-8{{y}^{2}}+8x-4y+12=0\] and the line \[x-y=2\] to the origin , makes the angles with the axes
  A)
             \[{{30}^{o}}\]and \[{{45}^{o}}\]                                       done clear
  B)
             \[{{45}^{o}}\] and \[{{60}^{o}}\] done clear
  C)
             Equal                                        done clear
  D)
             Parallel to axes done clear
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• question_answer9)
  The lines joining the points of intersection of the curve \[{{(x-h)}^{2}}+{{(y-k)}^{2}}-{{c}^{2}}=0\] and the line \[kx+hy=2hk\]  to the origin are perpendicular, then
  A)
             \[c=h\pm k\]                        done clear
  B)
             \[{{c}^{2}}={{h}^{2}}+{{k}^{2}}\] done clear
  C)
             \[{{c}^{2}}={{(h+k)}^{2}}\]      done clear
  D)
             \[4{{c}^{2}}={{h}^{2}}+{{k}^{2}}\] done clear
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• question_answer10)
  If the distance of two lines passing through origin from the point \[({{x}_{1}},{{y}_{1}})\] is \['d'\], then the equation of lines is
  A)
             \[{{(x{{y}_{1}}-y{{x}_{1}})}^{2}}={{d}^{2}}({{x}^{2}}+{{y}^{2}})\] done clear
  B)
             \[{{({{x}_{1}}{{y}_{1}}-xy)}^{2}}=({{x}^{2}}+{{y}^{2}})\] done clear
  C)
             \[{{(x{{y}_{1}}+y{{x}_{1}})}^{2}}=({{x}^{2}}-{{y}^{2}})\]       done clear
  D)
             \[({{x}^{2}}-{{y}^{2}})=2({{x}_{1}}+{{y}_{1}})\] done clear
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• question_answer11)
  The lines joining the origin to the points of intersection of the line \[3x-2y=1\] and the curve \[3{{x}^{2}}+5xy-3{{y}^{2}}+2x+3y=0\], are
  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)
             None of these done clear
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• question_answer12)
  The distance between the parallel lines \[9{{x}^{2}}-6xy+{{y}^{2}}+18x-6y+8=0\] is          [EAMCET 1994]
  A)
             \[1/\sqrt{10}\]                     done clear
  B)
             \[2/\sqrt{10}\] done clear
  C)
             \[4/\sqrt{10}\]                     done clear
  D)
             \[\sqrt{10}\] done clear
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• question_answer13)
  Two lines are given by\[{{(x-2y)}^{2}}+k(x-2y)=0\]. The value of k so that the distance between them is 3, is
  A)
             \[\frac{1}{\sqrt{5}}\]         done clear
  B)
             \[\pm \frac{2}{\sqrt{5}}\] done clear
  C)
             \[\pm 3\sqrt{5}\]                done clear
  D)
             None of these done clear
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• question_answer14)
  The pair of straight lines joining the origin to the points of intersection of the line \[y=2\sqrt{2}x+c\]and the circle \[{{x}^{2}}+{{y}^{2}}=2\]are at right angles, if                                     [MP PET 1996]
  A)
             \[{{c}^{2}}-4=0\]                  done clear
  B)
             \[{{c}^{2}}-8=0\] done clear
  C)
             \[{{c}^{2}}-9=0\]                  done clear
  D)
             \[{{c}^{2}}-10=0\] done clear
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• question_answer15)
  The equation \[8{{x}^{2}}+8xy+2{{y}^{2}}+26x+13y+15=0\] represents a pair of straight lines. The distance between  them is [UPSEAT 2001]
  A)
             \[7/\sqrt{5}\]                        done clear
  B)
             \[7/2\sqrt{5}\] done clear
  C)
             \[\sqrt{7}/5\]                        done clear
  D)
             None of these done clear
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• question_answer16)
  Distance between the pair of lines represented by the equation \[{{x}^{2}}-6xy+9{{y}^{2}}+3x-9y-4=0\]is  [Kerala (Engg,) 2002]
  A)
             \[\frac{15}{\sqrt{10}}\]     done clear
  B)
             \[\frac{1}{2}\] done clear
  C)
             \[\sqrt{\frac{5}{2}}\]         done clear
  D)
             \[\frac{1}{\sqrt{10}}\] done clear
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• question_answer17)
  The equation of pair of lines joining origin to the points of intersection of \[{{x}^{2}}+{{y}^{2}}=9\]and \[x+y=3\] is [MP PET 2004]
  A)
             \[{{(x+y)}^{2}}=9\]             done clear
  B)
             \[{{x}^{2}}+{{(3-x)}^{2}}=9\] done clear
  C)
             \[xy=0\]                                  done clear
  D)
             \[{{(3-x)}^{2}}+{{y}^{2}}=9\] done clear
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• question_answer18)
  The distance between the pair of parallel lines \[{{x}^{2}}+2xy+{{y}^{2}}-8ax-8ay-9{{a}^{2}}=0\] is  [Karnataka CET 2005]
  A)
             \[2\sqrt{5}a\]                       done clear
  B)
             \[\sqrt{10}\,a\] done clear
  C)
             \[10\,a\]                                 done clear
  D)
             \[5\sqrt{2}\,a\] done clear
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