Let the tangent and normal at the point \( (3\sqrt{3}, 1) \) on the ellipse \( \dfrac{x^2}{36} + \dfrac{y^2}{4} = 1 \) 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:
