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

  • question_answer
    The co-ordinates of pole of line \[lx+my+n=0\]with respect to circles \[{{x}^{2}}+{{y}^{2}}=1\], is                                              [RPET 1987]

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

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

    C)            \[\left( \frac{l}{n},-\frac{m}{n} \right)\]                                    

    D)            \[\left( -\frac{l}{n},\frac{m}{n} \right)\]

    Correct Answer: B

    Solution :

               Let pole be \[({{x}_{1}},{{y}_{1}})\] then polar                    will be \[x{{x}_{1}}+y{{y}_{1}}=1\] comparing with \[lx+my+n=0\]                    \[\Rightarrow {{x}_{1}}=-\frac{l}{n},\ {{y}_{1}}=-\frac{m}{n}\].


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