Aspire Faculty ID #18037 · Topic: JEE Main 2026 (24 January Morning Shift) · Just now
JEE Main 2026 (24 January Morning Shift)

Let a circle of radius $4$ pass through the origin $O$, the point $A(-\sqrt{3}a,0)$ and $B(0,-\sqrt{2}b)$, where $a$ and $b$ are real parameters and $ab\ne0$. Then the locus of centroid of $\triangle OAB$ is a circle of radius:

Solution

$AB=8$

$3a^2+2b^2=64$

Centroid $G(h,k)$

$h=\frac{-\sqrt{3}a}{3},\quad k=\frac{-\sqrt{2}b}{3}$

$a=-\sqrt{3}h,\quad b=-\frac{3k}{\sqrt{2}}$

Substitute

$9h^2+9k^2=64$

$x^2+y^2=\frac{64}{9}$

$\Rightarrow r=\frac{8}{3}$
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