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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 pole of the straight line \[x+2y=1\]with respect to the circle \[{{x}^{2}}+{{y}^{2}}=5\]is                                          [RPET 2000, 01]

    A)            (5, 5)                                         

    B)          (5, 10)

    C)            (10, 5)                                      

    D)            (10, 10)

    Correct Answer: B

    Solution :

                Let the pole be\[({{x}_{1}},{{y}_{1}})\], then the equation of polar is \[x{{x}_{1}}+y{{y}_{1}}={{a}^{2}}\]Þ\[x{{x}_{1}}+y{{y}_{1}}=5\]              ....(i)                    Since (i) and \[x+2y=1\] represents the same straight line . \[\therefore \] \[{{x}_{1}}=5\], \[{{y}_{1}}=10\] Þ Pole is (5, 10).


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