Ellipse

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 \(A B\) 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 :