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

  • question_answer
    For what value of k, the points (0, 0),      (1, 3), (2, 4) and (k, 3) are con-cyclic                                            [RPET 1997]

    A)            2    

    B)            1

    C)            4    

    D)            5

    Correct Answer: B

    Solution :

               The equation of circle through points (0, 0), (1, 3) and (2, 4) is                    \[{{x}^{2}}+{{y}^{2}}-10x=0\]                    Point \[(k,\,3)\] will be on the circle, if                    \[{{k}^{2}}+9-10k=0\Rightarrow {{k}^{2}}-10k+9=0\]                    \[{{k}^{2}}-9k-k+9=0\Rightarrow k(k-9)-1(k-9)=0\]                    \[\Rightarrow \] \[k=1\] or\[k=9\].


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