A) \[{{x}^{2}}+{{y}^{2}}+3y-13=0\]
B) \[{{x}^{2}}+{{y}^{2}}-3y+1=0\]
C) \[{{x}^{2}}+{{y}^{2}}-3x+1=0\]
D) \[5{{x}^{2}}+5{{y}^{2}}+6y+16=0\]
Correct Answer: B
Solution :
The required equation of circle is \[({{x}^{2}}+{{y}^{2}}-6)+\lambda ({{x}^{2}}+{{y}^{2}}-6y+8)=0\] ?.(i) It passes through \[(1,1)\]. \[\therefore \] \[(1+1-6)+\lambda (1+1-6+8)=0\] \[\Rightarrow \] \[-4+4\lambda =0\] \[\Rightarrow \] \[\lambda =1\] \[\therefore \] Required equation of circle is \[{{x}^{2}}+{{y}^{2}}-6+{{x}^{2}}+{{y}^{2}}-6y+8=0\] \[\Rightarrow \] \[2{{x}^{2}}+2{{y}^{2}}-6y+2=0\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}-3y+1=0\]
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