A) \[{{x}^{2}}+{{y}^{2}}-2x-4y+1=0\]
B) \[{{x}^{2}}+{{y}^{2}}-2x-4y+3=0\]
C) \[3\left( {{x}^{2}}+{{y}^{2}} \right)-2x-4y+1=0\]
D) None of these
Correct Answer: C
Solution :
[c] So let centroid is (h, k) \[h=\frac{cos\alpha +sin\alpha +1}{3},K=\frac{sin\alpha -cos\alpha +2}{3}\] \[\Rightarrow cos\alpha +sin\alpha =3h-1\] .....(i) \[\Rightarrow sin\alpha -cos\alpha =3k-2\] ?..(ii) Squaring and adding \[2={{\left( 3h-1 \right)}^{2}}+{{\left( 3k-2 \right)}^{2}}\] locus \[{{\left( 3x-1 \right)}^{2}}+{{\left( 3y-2 \right)}^{2}}=2\]
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