$(p, q)$ is the point of intersection of a latus rectum and an asymptote of the hyperbola $9 x^2-16 y^2=144$. If $p>0$ and $q>0$, then $q=$

The point of intersection of two tangents drawn to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{4}=1$ lie on the circle $x^2+y^2=5$. If these tangents are perpendicular to each other, then $a=$

If the line $2 x+\sqrt{6} y=2$ touches the hyperbola $x^2-2 y^2=4$, then the coordinates of the point of contact are

If the angle between the asymptotes of a hyperbola is $30^{\circ}$, then its eccentricity is