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

  • question_answer
    If the equation \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] represents a circle with x-axis as a diameter and radius a, then

    A)            \[f=2a,\ g=0,\ c=3{{a}^{2}}\]   

    B)            \[f=0,\ g=a,\ c=3{{a}^{2}}\]

    C)            \[f=0,\ g=-2a,\ c=3{{a}^{2}}\]  

    D)            None of these

    Correct Answer: C

    Solution :

               Here \[\sqrt{{{f}^{2}}+{{g}^{2}}-c}=a\]                    f must be zero; \[\Rightarrow {{g}^{2}}-c={{a}^{2}}\].


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