JEE Main 2022 · 28 Jul · Shift 1, Mathematics question 7

For $t\in(0,2\pi)$, if ABC is an equilateral triangle with vertices $A(\sin t,-\cos t)$, $B(\cos t,\sin t)$ and $C(a,b)$ such that its orthocentre lies on a circle with centre $\left(1,\dfrac13\right)$, then $\left(a^2-b^2\right)$ is equal to :