JEE Main 2023 — Ellipse Question with Solution

Let the tangent and normal at the point $$(3\sqrt{3},1)$$ on the ellipse $$\frac{x^2}{36}+\frac{y^2}{4}=1$$ meet the $$y$$-axis at the points $$A$$ and $$B$$ respectively. Let the circle $$C$$ be drawn taking $$AB$$ as a diameter and the line $$x=2\sqrt{5}$$ intersect $$C$$ at the points $$P$$ and $$Q$$. If the tangents at the points $$P$$ and $$Q$$ on the circle intersect at the point $$(\alpha ,\beta )$$, then $${\alpha }^2-{\beta }^2$$ is equal to :