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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 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)                                        

    B)            (-2, -2)

    C)            (- 2, 2)                                     

    D)            (2, -2)

    Correct Answer: C

    Solution :

               Putting \[X=x+2,\ \ Y=y-2\]            Equation becomes\[2{{X}^{2}}+3XY-2{{Y}^{2}}=0\]            Which cuts at \[X=0,\ Y=0\]            So, \[x+2=0,\ y-2=0\]            Point of intersection\[(-2,2)\].            Trick: Only (-2, 2) is satisfying the given equation.


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