Ellipse

Let an ellipse \(E:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\), \({a^2} > {b^2}\), passes through \(\left( {\sqrt {{3 \over 2}} ,1} \right)\) and has eccentricity \({1 \over {\sqrt 3 }}\). If a circle, centered at focus F(\(\alpha\), 0), \(\alpha\) > 0, of E and radius \({2 \over {\sqrt 3 }}\), intersects E at two points P and Q, then PQ² is equal to :