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

The equation of the pair of asymptotes of the hyperbola $4x^2 - 9y^2 - 24x - 36y - 36 = 0$ is

If $(a - 2)x^2 + ay^2 = 4$ represents a rectangular hyperbola,then $a$ equals:

Let $P(a \sec \theta, b \tan \theta)$ and $Q(a \sec \phi, b \tan \phi)$ be two points such that $\theta+\phi=\frac{\pi}{2}$ on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If $(h, k)$ is the point of intersection of the normals at $P$ and $Q$,then $k=$

The equation of the pair of asymptotes of the hyperbola $x^2-2 y^2-8 x+8 y+4=0$ is

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 $k=$