What is the length of the latus rectum of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = -1$?

$A$ common tangent to $9x^{2}-16y^{2}=144$ and $x^{2}+y^{2}=9$ is

The angle between the tangents drawn from $(1, 2\sqrt{2})$ to the hyperbola $16x^{2} - 25y^{2} = 400$ is.....

The line $2x + y = 1$ is a tangent to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ $(a > b)$. If this line passes through the point of intersection of a directrix and the positive $X$-axis,then the eccentricity of that hyperbola is

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

$A$ 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: