The eccentricity of the hyperbola $\frac{{{x^2}}}{{16}} - \frac{{{y^2}}}{{25}} = 1$ is

The locus of the mid points of the chords of the hyperbola $\mathrm{x}^{2}-\mathrm{y}^{2}=4$, which touch the parabola $\mathrm{y}^{2}=8 \mathrm{x}$, is :

The difference of the focal distance of any point on the hyperbola $9{x^2} - 16{y^2} = 144$, is

If area of quadrilateral formed by tangents  drawn at ends of latus rectum of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is equal to square of distance between centre and one  focus of hyperbola, then $e^3$ is ($e$ is eccentricity of hyperbola)

The locus of the centroid of the triangle formed by any point $\mathrm{P}$ on the hyperbola $16 \mathrm{x}^{2}-9 \mathrm{y}^{2}+$ $32 x+36 y-164=0$, and its foci is:

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 major and minor axes of the ellipse, respectively. If the product of their eccentricities in one, then the equation of the hyperbola is ...... .