A) (3, 3)
B) \[(2,\,\,-1)\]
C) \[(-2,\,\,1)\]
D) \[(-1,\,\,2)\]
Correct Answer: B
Solution :
\[x=2+3\cos \theta ,y=3\sin \theta -1\] \[{{x}^{2}}+{{y}^{2}}=4+9{{\cos }^{2}}\theta +12\cos \theta +9{{\sin }^{2}}\theta +1-6\sin \theta \] \[=14+12\cos \theta -6\sin \theta \] =\[4(2+3\cos \theta )-2(3\sin \theta -1)+4\] Þ \[{{x}^{2}}+{{y}^{2}}=4x-2y+4\] Þ \[({{x}^{2}}-4x+4)+({{y}^{2}}+2y+1)=9\] Þ \[{{(x-2)}^{2}}+{{(y+1)}^{2}}=9\], \ centre is \[(2,-1)\].
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