If the latus rectum subtends a right angle at the center of the hyperbola,then its eccentricity is

If $l_1$ and $l_2$ are the lengths of the perpendiculars drawn from a point on the hyperbola $5x^2 - 4y^2 - 20 = 0$ to its asymptotes,then $\frac{l_1^2 l_2^2}{100} = $

Let $P(3 \sec \theta, 2 \tan \theta)$ and $Q(3 \sec \phi, 2 \tan \phi)$ be two points on the hyperbola $\frac{x^2}{9} - \frac{y^2}{4} = 1$ such that $\theta + \phi = \frac{\pi}{2}$ where $0 < \theta, \phi < \frac{\pi}{2}$. Then the ordinate of the point of intersection of the normals at $P$ and $Q$ is:

If $P(x_1, y_1)$ is a point on the hyperbola $x^2 - y^2 = a^2$,then $SP \cdot S'P = \_\_\_\_$

Let $P (3 \sec \theta, 2 \tan \theta)$ and $Q (3 \sec \phi, 2 \tan \phi)$ where $\theta + \phi = \frac{\pi}{2}$,be two distinct points on the hyperbola $\frac{x^2}{9} - \frac{y^2}{4} = 1$. Then the ordinate of the point of intersection of the normals at $P$ and $Q$ is

If the coordinates of a point are given by the equations $x = b \sec \phi$ and $y = a \tan \phi$,then its locus is