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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Equations of circle, Geometrical problems regarding circle

  • question_answer
    The four distinct points (0, 0),(2, 0), (0, -2) and (k, -2)are con-cyclic, if k =                                  [EAMCET 2002]

    A) - 2  

    B) 2

    C) 1    

    D) 0

    Correct Answer: B

    Solution :

    The equation of circle passing through \[(0,\,0),\,\,(2,\,0)\] and (0, ? 2) is \[{{x}^{2}}+{{y}^{2}}-2x+2y=0\]. If it passes through \[(k,\,-2)\], then \[{{k}^{2}}+4-2k-4=0\]\[\Rightarrow \,k=0,\,2\]            \[\because \]\[(0,\,-2)\] is already a point on circle \[\therefore \] k = 2.


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