The line x=8 is the directrix of the ellipse E: x^2/(a^2)+y^2/(b^2)=1 with the corresponding focus (2,0). If the tangent to E at the point P in the…

The line $\displaystyle x=8$ is the directrix of the ellipse $\displaystyle \mathrm{E}: \frac{x^2}{\mathrm{a}^2}+\frac{y^2}{\mathrm{~b}^2}=1$ with the corresponding focus $\displaystyle (2,0)$. If the tangent to E at the point P in the first quadrant passes through the point $\displaystyle (0,4 \sqrt{3})$ and intersects the $\displaystyle x$-axis at Q , then $\displaystyle (3 \mathrm{PQ})^2$ is equal to $\displaystyle \_\_\_\_$.