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JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank Bisectors of the angle between the lines, Point of intersection of the lines

  • question_answer
    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)            \[y=x\]                                   

    B)            \[y=-x\]

    C)            \[y=mx\]                               

    D)            \[my=x\]

    Correct Answer: C

    Solution :

               Equation of bisectors of angle between the lines represented by \[p{{x}^{2}}-2rxy+q{{y}^{2}}=0\]is            \[\frac{{{x}^{2}}-{{y}^{2}}}{p-q}=\frac{xy}{-r}\]                                                       ..... (i)               On putting \[y=mx\]in (i), we get            \[\frac{1-{{m}^{2}}}{p-q}=\frac{m}{-r}\]\[\Rightarrow r(1-{{m}^{2}})+m(p-q)=0\].


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