The eccentricity of the curve $x^2 - y^2 = a^2$ is

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

The Cartesian form of the curve given by $x = \frac{a}{2} (t + \frac{1}{t})$ and $y = \frac{a}{2} (t - \frac{1}{t})$,where $t$ is a parameter,is:

If a hyperbola passes through the point $P(10, 16)$ and it has vertices at $(\pm 6, 0)$,then the equation of the normal to it at $P$ is

The locus of the point of intersection of the lines $ax \sec \theta + by \tan \theta = a$ and $ax \tan \theta + by \sec \theta = b$,where $\theta$ is the parameter,is

The eccentricity of the hyperbola $25x^2 - 9y^2 = 225$ is...