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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Chord of contact of tangent, Pole and Polar

  • question_answer
    The equation of the diameter of the circle \[{{x}^{2}}+{{y}^{2}}+2x-4y-11=0\]which bisects the chords intercepted on the line \[2x-y+3=0\]is

    A)            \[x+y-7=0\]                             

    B)            \[2x-y-5=0\]

    C)            \[x+2y-3=0\]                          

    D)            None of these

    Correct Answer: C

    Solution :

               We know that the diameter will be perpendicular to the chord because it bisects the chord. Hence the equation of diameter is \[x+2y+k=0\]   ?.(i)                    But (i) also passes through the centre of circle \[(-1,\ 2)\]. Therefore, \[-1+4+k=0\Rightarrow k=-3\].                    Hence the required equation is \[x+2y-3=0\].


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