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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank System of circles

  • question_answer
    If the circles \[{{x}^{2}}+{{y}^{2}}-2ax+c=0\] and \[{{x}^{2}}+{{y}^{2}}+2by+2\lambda =0\] intersect orthogonally, then the value of \[\lambda \]is

    A)            c     

    B)            - c

    C)            0    

    D)            None of these

    Correct Answer: D

    Solution :

               Condition for circle intersects orthogonally,                    \[2({{g}_{1}}{{g}_{2}}+{{f}_{1}}{{f}_{2}})={{c}_{1}}+{{c}_{2}}\]\[\Rightarrow 0=c+2\lambda \Rightarrow \lambda =-\frac{c}{2}\] .


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