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

  • question_answer
    The circle represented by the equation \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] will be a point circle, if

    A)            \[{{g}^{2}}+{{f}^{2}}=c\]     

    B)            \[{{g}^{2}}+{{f}^{2}}>c\]

    C)            \[{{g}^{2}}+{{f}^{2}}+c=0\]                                           

    D)            None of these

    Correct Answer: A

    Solution :

               Using condition of point circle                    \[R=\sqrt{{{g}^{2}}+{{f}^{2}}-c}=0\Rightarrow {{g}^{2}}+{{f}^{2}}=c\].


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