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…

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

[JEE Main 2023, 13 Apr (Shift 1)]