$A$ point on the curve $\frac{x^2}{A^2} - \frac{y^2}{B^2} = 1$ is

The length of the latus rectum of the hyperbola $25x^2 - 16y^2 = 400$ is -

If $e$ and $e'$ are the eccentricities of a hyperbola and its conjugate hyperbola respectively,then:

Let $A(\theta_1)$ and $B(\theta_2)$ be two points on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and $S$ be the focus of the hyperbola. If $A, S, B$ are collinear and $a \cos \left(\frac{\theta_1+\theta_2}{2}\right)=k \cos \left(\frac{\theta_1-\theta_2}{2}\right)$ then $k=$

If the straight line $x \cos \alpha + y \sin \alpha = p$ is a tangent to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,then:

If $c$ is a real number and $\frac{x^2}{c-12}+\frac{y^2}{7-c}=1$ represents a hyperbola,then