A) \[{{x}^{2}}+{{y}^{2}}=9{{a}^{2}}\]
B) \[{{x}^{2}}+{{y}^{2}}=16{{a}^{2}}\]
C) \[{{x}^{2}}+{{y}^{2}}=16{{a}^{2}}\]
D) \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]
Correct Answer: C
Solution :
Key Idea: Centroid divides the median in the ratio of\[2:1\]. Given, circle has centre at origin and passing through vertices of equilateral \[\Delta \] whose median is of length\[3a\]. \[\therefore \]Radius\[=3a\cdot \frac{2}{3}=2a\] \[\Rightarrow \]Equation of circle \[{{(x-0)}^{2}}+{{(y-0)}^{2}}={{(2a)}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}=4{{a}^{2}}\]You need to login to perform this action.
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