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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Tangent and normal to a circle

  • question_answer
    An infinite number of tangents can be drawn from (1, 2) to the circle \[{{x}^{2}}+{{y}^{2}}-2x-4y+\lambda =0\], then \[\lambda =\] [MP PET 1989]

    A)            ? 20                                          

    B)            0

    C)            5    

    D)            Cannot be determined

    Correct Answer: C

    Solution :

               Clearly the point (1, 2) is the centre of the given circle and infinite tangents can only be drawn on a point circle. Hence radius should be 0.                    \[\therefore \,\sqrt{{{1}^{2}}+{{2}^{2}}-\lambda }=0\Rightarrow \lambda =5\].


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