What kind of hyperbola does the equation $9x^2 - 16y^2 - 18x + 32y - 151 = 0$ represent?

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

$A$ tangent to the curve $9 b^2 x^2 - 4 a^2 y^2 = 36 a^2 b^2$ makes intercepts of unit length on each of the coordinate axes. Then the point $(a, b)$ lies on:

If the line $lx + my = 1$ is a normal to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,then $\frac{a^2}{l^2} - \frac{b^2}{m^2}$ is equal to

Let the product of the focal distances of the point $P(4, 2\sqrt{3})$ on the hyperbola $H: \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ be $32$. Let the length of the conjugate axis of $H$ be $p$ and the length of its latus rectum be $q$. Then $p^2 + q^2$ is equal to ......

$A$ hyperbola passes through a focus of the ellipse $\frac{x^2}{169}+\frac{y^2}{25}=1$. Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse. The product of their eccentricities is $1$. Then,the equation of the hyperbola is