The length of the latus rectum and directrices of a hyperbola with eccentricity e are 9 and x= ± 4/(√ 3), respectively. Let the line y-√ 3 x+√ 3 =0…

The length of the latus rectum and directrices of a hyperbola with eccentricity e are $\displaystyle 9$ and $\displaystyle x= \pm \frac{4}{\sqrt{3}}$, respectively. Let the line $\displaystyle y-\sqrt{3} x+\sqrt{3}=0$ touch this hyperbola at $\displaystyle \left(x_0, y_0\right)$. If $\displaystyle m$ is the product of the focal distances of the point $\displaystyle \left(x_0, y_0\right)$, then $\displaystyle 4 \mathrm{e}^2+\mathrm{m}$ is equal to $\displaystyle \_\_\_\_$.