If \[A(\cos \alpha ,\sin \alpha ),\ B(\sin \alpha ,-\cos \alpha ),\,C(1,\text{ }2)\]are the vertices of a \[\Delta ABC\], then as \[\alpha \]varies, the locus of its centroid is

\[{{x}^{2}}+{{y}^{2}}-2x-4y+3=0\]

\[{{x}^{2}}+{{y}^{2}}-2x-4y+1=0\]

\[3({{x}^{2}}+{{y}^{2}})-2x-4y+1=0\]

If \[A(\cos \alpha ,\sin \alpha ),\ B(\sin \alpha ,-\cos \alpha ),\,C(

1.	If \[A(\cos \alpha ,\sin \alpha ),\ B(\sin \alpha ,-\cos \alpha ),\,C(1,\text{ }2)\]are the vertices of a \[\Delta ABC\], then as \[\alpha \]varies, the locus of its centroid is
A.	\[{{x}^{2}}+{{y}^{2}}-2x-4y+1=0\]
B.	\[3({{x}^{2}}+{{y}^{2}})-2x-4y+1=0\]
C.	\[{{x}^{2}}+{{y}^{2}}-2x-4y+3=0\]
D.	None of these
Answer» C. \[{{x}^{2}}+{{y}^{2}}-2x-4y+3=0\]

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If \[A(\cos \alpha ,\sin \alpha ),\ B(\sin \alpha ,-\cos \alpha ),\,C(1,\text{ }2)\]are the vertices of a \[\Delta ABC\], then as \[\alpha \]varies, the locus of its centroid is

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