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

  • question_answer
    The equation of the circle which intersects circles \[{{x}^{2}}+{{y}^{2}}+x+2y+3=0\],\[{{x}^{2}}+{{y}^{2}}+2x+4y+5=0\]and \[{{x}^{2}}+{{y}^{2}}-7x-8y-9=0\] at right angle, will be

    A)            \[{{x}^{2}}+{{y}^{2}}-4x-4y-3=0\]                                

    B)            \[3({{x}^{2}}+{{y}^{2}})+4x-4y-3=0\]

    C)            \[{{x}^{2}}+{{y}^{2}}+4x+4y-3=0\]

    D)            \[3({{x}^{2}}+{{y}^{2}})+4(x+y)-3=0\]

    Correct Answer: D

    Solution :

     Let circle be\[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]. Then according to the conditions given, \[g+2f=c+3\]                                                                      ?. (i)                    \[2g+4f=c+5\]                                                 ?. (ii)                    \[-7g-8f=c-9\]                                                 ?. (iii)                    \[\Rightarrow g=\frac{2}{3},\ f=\frac{2}{3},\ c=-1\]                    Therefore, the required equation is                    \[3({{x}^{2}}+{{y}^{2}})+4(x+y)-3=0\].


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