A) \[{{x}^{2}}+{{y}^{2}}-6x+12y-15=0\]
B) \[{{x}^{2}}+{{y}^{2}}-6x+12y+15=0\]
C) \[{{x}^{2}}+{{y}^{2}}-6x+12y+45=0\]
D) None of these
Correct Answer: A
Solution :
Equation of circle concentric to given circle is \[{{x}^{2}}+{{y}^{2}}-6x+12y+k=0\] ?. (i) Radius of circle (i) \[=\sqrt{2}\] (radius of given circle) \[\Rightarrow \sqrt{9+36-k}=\sqrt{2}\sqrt{9+36-15}\] \[\Rightarrow 45-k=60\Rightarrow k=-15\] Hence the required equation of circle is \[{{x}^{2}}+{{y}^{2}}-6x+12y-15=0\].
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