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

If $\theta$ is the angle between the asymptotes of the hyperbola $\frac{x^2}{a^2}-\frac{(y-2)^2}{4}=1$ and $\cos \theta=\frac{5}{13}$,then $a^2=$

If the variable line $y = kx + 2h$ is tangent to an ellipse $2x^2 + 3y^2 = 6$,the locus of $P(h, k)$ is a conic $C$ whose eccentricity equals

The equation of the tangents to the hyperbola $3x^2 - 4y^2 = 12$ which cut equal intercepts from the axes are:

Let the hyperbola be $x^2 - 2y^2 - 2\sqrt{2}x - 4\sqrt{2}y - 6 = 0$. Let $A$ be a vertex of the hyperbola. Let $B$ be an endpoint of the latus rectum near $A$. If $C$ is the focus of the hyperbola nearest to $A$,find the area of triangle $ABC$.

Let $P (3 \sec \theta, 2 \tan \theta)$ and $Q (3 \sec \phi, 2 \tan \phi)$ where $\theta + \phi = \frac{\pi}{2}$,be two distinct points on the hyperbola $\frac{x^2}{9} - \frac{y^2}{4} = 1$. Then the ordinate of the point of intersection of the normals at $P$ and $Q$ is