Let an ellipse E: x^2/(a^2)+y^2/(b^2)=1, a^2> b^2, passes through (√(3/2), 1) and has eccentricity 1/(√ 3). If a circle, centered at focus F (α, 0),…

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