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

  • question_answer
    A line \[lx+my+n=0\]meets the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]at the points P and Q. The tangents drawn at the points P and Q meet at R, then the coordinates of R is

    A)            \[\left( \frac{{{a}^{2}}l}{n},\frac{{{a}^{2}}m}{n} \right)\]           

    B)            \[\left( \frac{-{{a}^{2}}l}{n},\frac{-{{a}^{2}}m}{n} \right)\]

    C)            \[\left( \frac{{{a}^{2}}n}{l},\frac{{{a}^{2}}n}{m} \right)\]           

    D)            None of these

    Correct Answer: B

    Solution :

               Suppose point be (h, k). Equation of common chord of contact is                    \[hx+ky-{{a}^{2}}=0\equiv lx+my+n=0\]                    or \[\frac{h}{l}=\frac{k}{m}=\frac{-{{a}^{2}}}{n}\] or \[h=\frac{-{{a}^{2}}l}{n}\], \[k=\frac{-{{a}^{2}}m}{n}\].


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