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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
    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

    B)            2

    C)  \[-2\]      

    D)            -1/2

    Correct Answer: C

    Solution :

               Here one equation of bisector is \[x-2y=0.\]We know that both bisectors are perpendicular, therefore second bisector will be \[2x+y=0\]because it passes through origin.            Hence the combined equations of bisectors is given by \[(2x+y)(x-2y)=0\Rightarrow -2{{x}^{2}}+3xy+2{{y}^{2}}=0.\]            Now comparing it by \[h{{x}^{2}}+3xy-h{{y}^{2}}=0\], we get h = ?2.


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