$A=\left(\cos \theta , \sin \theta \right)$ and $B=(\sin \theta ,-\cos \theta )$ are two points The locus of the centroid of $\mathrm{△}OAB$ where $O$ is the origin is

Let  $(h, k)$ be the centroid of $\mathrm{△}OAB$

$\therefore (h,k)=\left(\frac{\cos \theta +\sin \theta }{3},\frac{\sin \theta -\cos \theta }{3}\right)\Rightarrow 3h=\cos \theta +\sin \theta ,3k=\sin \theta -\cos \theta$$9h^2+9k^2=(\cos \theta +\sin \theta {)}^2+(\sin \theta -\cos \theta {)}^2\Rightarrow 9\left(h^2+k^2\right)=2$

Locus of $(h,k)\text{ is }9x^2+9y^2=2$