The eccentricity of a rectangular hyperbola is:

If the eccentricity of the hyperbola $\frac{x^2}{9} - \frac{y^2}{b^2} = 1$ passing through the point $(k, 2)$ is $\frac{\sqrt{13}}{3}$,then the value of $k^2$ is:

If $x = 9$ is the chord of contact of the hyperbola $x^2 - y^2 = 9$,then the equation of the corresponding pair of tangents is

If the vertices of a hyperbola are at $(-2, 0)$ and $(2, 0)$ and one of its foci is at $(-3, 0)$,then which one of the following points does not lie on this hyperbola?

Let the eccentricity $e$ of a hyperbola satisfy the equation $6e^2 - 11e + 3 = 0$. If the foci of the hyperbola are $(3, 5)$ and $(3, -4)$, then the length of its latus rectum is:

The length of the latus rectum of the curve $xy = 7x + 5y$ is