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

  • question_answer
    If \[{{x}^{2}}+{{y}^{2}}+px+3y-5=0\] and \[{{x}^{2}}+{{y}^{2}}+5x\] \[+py+7=0\] cut orthogonally, then p is

    A)            \[\frac{1}{2}\]                          

    B)            1

    C)            \[\frac{3}{2}\]                          

    D)            2

    Correct Answer: A

    Solution :

               \[2{{g}_{1}}{{g}_{2}}+2{{f}_{1}}{{f}_{2}}={{c}_{1}}+{{c}_{2}}\] for orthogonal cut.                    \[\Rightarrow p\,\,\left( \frac{5}{2} \right)+p\,\,\left( \frac{3}{2} \right)=-5+7\Rightarrow p=\frac{1}{2}\].


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