Let the tangent and normal at the point (3 √ 3, 1) on the ellipse x^2/36+y^2/4=1 meet the y -axis at the points A and B respectively. Let the circle…

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