Let an ellipse E:x2a2+y2b2=1, a2>b2, passes through (√32,1), and has eccentricity1√3. If a circle, centered at focus F(α,0), (α>0), of E and radius 2√3, intersects E at two points P and Q, then PQ2 is equal to

Let an ellipse E:x2a2+y2b2=1, a2>b2, passes through (√32,1), and has

1.	Let an ellipse E:x2a2+y2b2=1, a2>b2, passes through (√32,1), and has eccentricity1√3. If a circle, centered at focus F(α,0), (α>0), of E and radius 2√3, intersects E at two points P and Q, then PQ2 is equal to
Answer» Let an ellipse $E : \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1,$ $a^{2} > b^{2},$ passes through $(\sqrt{\frac{3}{2}}, 1)$ , and has eccentricity $\frac{1}{\sqrt{3}}$ . If a circle, centered at focus $F (α, 0),$ $(α > 0),$ of $E$ and radius $\frac{2}{\sqrt{3}}$ , intersects $E$ at two points $P$ and $Q,$ then $P Q^{2}$ is equal to