The vertices of a hyperbola H are ( ± 6,0) and its eccentricity is (√ 5)/2. Let N be the normal to H at a point in the first quadrant and parallel to…

The vertices of a hyperbola H are $\displaystyle ( \pm 6,0)$ and its eccentricity is $\displaystyle \frac{\sqrt{5}}{2}$. Let N be the normal to H at a point in the first quadrant and parallel to the line $\displaystyle \sqrt{2} x+y=2 \sqrt{2}$. If d is the length of the line segment of N between H and the y -axis then $\displaystyle \mathrm{d}^2$ is equal to $\displaystyle \_\_\_\_$.