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

The product of the lengths of the perpendiculars drawn from any point on the hyperbola $x^2 - 2y^2 - 2 = 0$ to its asymptotes is

The equation of the chord of the hyperbola $25x^{2} - 16y^{2} = 400$ whose midpoint is $(5, 3)$ is:

If the eccentricity of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ is $\frac{5}{4}$ and $2x+3y-6=0$ is a focal chord of the hyperbola,then the length of the transverse axis is equal to

Let the domain of the function $f(x) = \log_{3}\log_{5}\log_{7}(9x - x^{2} - 13)$ be the interval $(m, n)$. Let the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ have eccentricity $\frac{n}{3}$ and the length of the latus rectum $\frac{8m}{3}$. Then $b^{2} - a^{2}$ is equal to:

If a hyperbola has length of its conjugate axis equal to $5$ and the distance between its foci is $13$,then the eccentricity of the hyperbola is