The eccentricity of the hyperbola which passes through the points $(3,0)$ and $(3\sqrt{2}, 2)$ is

The eccentricity of the hyperbola $2x^2 - y^2 = 6$ is

If $5x + 9 = 0$ is the directrix of the hyperbola $16x^2 - 9y^2 = 144,$ then its corresponding focus is

Consider a branch of the hyperbola $x^2 - 2y^2 - 2\sqrt{2}x - 4\sqrt{2}y - 6 = 0$ with vertex at the point $A$. Let $B$ be one of the end points of its latus rectum. If $C$ is the focus of the hyperbola nearest to the point $A$,then the area of the triangle $ABC$ is

The lines of the form $x \cos \phi + y \sin \phi = P$ are chords of the hyperbola $4x^2 - y^2 = 4a^2$ which subtend a right angle at the centre of the hyperbola. If these chords touch a circle with centre at $(0,0)$,then the radius of that circle is

Let $P(3 \sec \theta, 2 \tan \theta)$ and $Q(3 \sec \phi, 2 \tan \phi)$ be two points on the hyperbola $\frac{x^2}{9} - \frac{y^2}{4} = 1$ such that $\theta + \phi = \frac{\pi}{2}$ where $0 < \theta, \phi < \frac{\pi}{2}$. Then the ordinate of the point of intersection of the normals at $P$ and $Q$ is: