CircleHard
Question
Let a circle of radius 4 pass through the origin O , the points $A( - \sqrt{3}a,0)$ and $B(0, - \sqrt{2}\text{ }b)$, where $a$ and $b$ are real parameters and $ab \neq 0$. Then the locus of the centroid of $\bigtriangleup OAB$ is a circle of radius
Options
A.$\frac{5}{3}$
B.$\frac{7}{3}$
C.$\frac{8}{3}$
D.$\frac{11}{3}$
Solution
$$\begin{matrix} & AB = 8 \\ & 3a^{2} + 2b^{2} = 64 \end{matrix}$$
Centroid $G(h,k)$
$${h = - \frac{\sqrt{3}a}{3},k = - \frac{\sqrt{2}b}{3} }{a = - \sqrt{3}\text{ }h,\text{ }b = \frac{- 3}{\sqrt{2}}k }{9h^{2} + 9k^{2} = 64 }{x^{2} + y^{2} = \frac{64}{9} }{r = \frac{8}{3}}$$
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