A) \[{{x}^{2}}+{{y}^{2}}-3x-y-\frac{29}{2}=0\]
B) \[2{{x}^{2}}+2{{y}^{2}}+2x-5y-\frac{29}{2}=0\]
C) \[2{{x}^{2}}+2{{y}^{2}}-6x-2y-21=0\]
D) None of these
Correct Answer: C
Solution :
Required circle is \[(2{{x}^{2}}+2{{y}^{2}}-2x-6y-25)+\lambda (x-y-1)=0\] Its centre is\[\left( \frac{1-\lambda }{4},\ \frac{3-\lambda }{4} \right)\] lies on line\[x-y-1=0\]. Hence we get the equation of circle \[2{{x}^{2}}+2{{y}^{2}}-6x-2y-21=0\].
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