A) \[{{x}^{2}}+{{y}^{2}}=9{{a}^{2}}\]
B) \[{{x}^{2}}+{{y}^{2}}=16{{a}^{2}}\]
C) \[{{x}^{2}}+{{y}^{2}}=4{{a}^{2}}\]
D) \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]
Correct Answer: C
Solution :
We know that centroid divides the median in the ratio 2:1. Radius of the circle \[=\frac{2}{3}\times \]length of median \[=\frac{2}{3}\times 3a=2a\]Centre of the (given) circle is C(0, 0). Therefore the equation of the circle \[{{(x-0)}^{2}}+{{(y-0)}^{2}}={{(2a)}^{2}}\Rightarrow {{x}^{2}}+{{y}^{2}}=4{{a}^{2}}\]
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