Let a circle of radius 4 pass through the origin O , the points $A( - \sqrt{3}a,0)$ and $B(0, - \sqr

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Let a circle of radius 4 pass through the origin O , the points $A( - \sqrt{3}a,0)$ and $B(0, - \sqrt{2}	ext{ }b)$, where $a$ and $b$ are real parameters and $ab 
eq 0$. Then the locus of the centroid of $\bigtriangleup OAB$ is a circle of radius

Accepted Answer

$$\begin{matrix} & AB = 8 \ & 3a^{2} + 2b^{2} = 64 \end{matrix}$$Centroid $G(h,k)$$${h = - \frac{\sqrt{3}a}{3},k = - \frac{\sqrt{2}b}{3} }{a = - \sqrt{3}	ext{ }h,	ext{ }b = \frac{- 3}{\sqrt{2}}k }{9h^{2} + 9k^{2} = 64 }{x^{2} + y^{2} = \frac{64}{9} }{r = \frac{8}{3}}$$

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