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

  • question_answer
     If the radius of the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] be r, then it will touch both the axes, if

    A)            \[g=f=r\]                                  

    B)            \[g=f=c=r\]

    C)            \[g=f=\sqrt{c}=r\]                  

    D)            \[g=f\] and \[{{c}^{2}}=r\]

    Correct Answer: C

    Solution :

     Conditions are \[g=f=r\] and\[\sqrt{{{g}^{2}}+{{f}^{2}}-c}=r\] \[\Rightarrow g=\sqrt{c}\].


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