Let a circle of radius 4 pass through the origin O, the points and where and are real parameters and . Then the locus of the centroid of is a circle of radius [2026]

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Solution

Q.
Let a circle of radius 4 pass through the origin O, the points $A (- \sqrt{3} a, 0)$ and $B (0, - \sqrt{2} b),$ where $a$ and $b$ are real parameters and $a b \neq 0$ . Then the locus of the centroid of $∆ O A B$ is a circle of radius [2026]

1 $\frac{7}{3}$

2 $\frac{8}{3}$

3 $\frac{5}{3}$

4 $\frac{11}{3}$

Ans.
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