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JEE Main & Advanced Mathematics Straight Line Question Bank Angle between two straight lines, Bisector of angle between two lines

  • question_answer
    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)            \[3x=19\]                                 

    B)            \[3y=7\]

    C)            \[3x=19\]and \[3y=7\]           

    D) None of these

    Correct Answer: A

    Solution :

    Since the origin and the point (1, ?3) lie on the same side of \[x+2y-11=0\] and on the opposite side of \[3x-6y-5=0\]. Therefore, the bisector of the angle containing \[(1,-3)\] is the bisector of that angle which does not contain the origin and is given by \[\frac{-x-2y+11}{\sqrt{5}}=-\left( \frac{-3x+6y+5}{\sqrt{45}} \right)\] i.e., \[3x=19\].


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