Coordinate Geometry: JEE Main 2026 Mathematics question

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 $ab \ne 0$. Then the locus of the centroid of $\triangle OAB$ is a circle of radius