Find the equation of the hyperbola whose foci are $(6, 5)$ and $(-4, 5)$ and eccentricity is $5/4$.

Let $H : \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$,$a > 0, b > 0$,be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is $4(2\sqrt{2}+\sqrt{14})$. If the eccentricity of $H$ is $\frac{\sqrt{11}}{2}$,then the value of $a^{2}+b^{2}$ is equal to

Let $a$ and $b$ respectively be the semi-transverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation $9e^2 - 18e + 5 = 0$. If $S(5, 0)$ is a focus and $5x = 9$ is the corresponding directrix of this hyperbola,then $a^2 - b^2$ is equal to

If the latus rectum of a hyperbola through one focus subtends an angle of $60^{\circ}$ at the other focus,then its eccentricity is

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

The locus of the midpoints of the parallel chords with gradient $m$ of the rectangular hyperbola $xy = c^2$ is