Mathematics Question from JEE Main 2023 · 13 April, Shift 1

Let the tangent and normal at the point $\left( 3\sqrt{3}, 1 \right)$ 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: