A) \[3{{x}^{2}}+3{{y}^{2}}-8x-13y=0\]
B) \[3{{x}^{2}}+3{{y}^{2}}-8x+29y=0\]
C) \[3{{x}^{2}}+3{{y}^{2}}+8x+29y=0\]
D) \[3{{x}^{2}}+3{{y}^{2}}-8x-29y=0\]
Correct Answer: B
Solution :
Let the required equation of circle be\[{{x}^{2}}+{{y}^{2}}+2gx+2fy=0\]. Since, the above circle cuts the given circles orthogonally. \[\therefore \]\[2(-3g)+2f(0)=8\] \[\Rightarrow \] \[2g=-\frac{8}{3}\] and \[-2g-2f=-7\] \[\Rightarrow \] \[2f=+7+\frac{8}{3}=\frac{29}{3}\] \[\therefore \]Required equation of circle is \[{{x}^{2}}+{{y}^{2}}-\frac{8}{3}x+\frac{29}{3}y=0\] or \[3{{x}^{2}}+3{{y}^{2}}-8x+29y=0\]
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