If $P$ is a point on the hyperbola $16x^2 - 9y^2 = 144$ whose foci are $S_1$ and $S_2$,then $|PS_1 - PS_2| = $

Find the equation of the hyperbola satisfying the given conditions: Vertices $(\pm 2, 0)$,foci $(\pm 3, 0)$.

If a hyperbola passes through the foci of the ellipse $\frac{x^2}{25} + \frac{y^2}{16} = 1$ and its transverse and conjugate axes coincide with the major and minor axes of the ellipse respectively,and the product of their eccentricities is $1$,then:

Circles are drawn on chords of the rectangular hyperbola $xy = c^2$ parallel to the line $y = x$ as diameters. All such circles pass through two fixed points whose coordinates are:

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

The length of the latus rectum of the hyperbola $\frac{x^2}{\cos^2 \alpha} - \frac{y^2}{\sin^2 \alpha} = 4$ is (where $\alpha \neq \frac{n\pi}{2}, n \in I$).