Hyperbola

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