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

  • question_answer
    The point of contact of the tangent to the circle \[{{x}^{2}}+{{y}^{2}}=5\]at the point (1, ?2) which touches the circle \[{{x}^{2}}+{{y}^{2}}-8x+6y+20=0\], is                                                                [Roorkee 1989]

    A)            (2, -1)                                       

    B)            (3, -1)

    C)            (4, -1)                                       

    D)            (5, -1)

    Correct Answer: B

    Solution :

               Equation of the tangent at \[(1,\ -2)\] to the circle \[{{x}^{2}}+{{y}^{2}}=1\] is \[x-2y=5\]. Now choose answers. Here, only point (3, ?1) lies on the tangent.


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