If $e_{1}$ and $e_{2}$ are the eccentricities of a hyperbola $3x^{2} - 3y^{2} = 25$ and its conjugate,then

The eccentricity of the hyperbola $5x^2 - 4y^2 + 20x + 8y = 4$ is

If $P(\theta) = (x_1, \frac{3 \sqrt{5}}{2})$,$0 < \theta < \frac{\pi}{2}$ is a point on the hyperbola $\frac{x^2}{25} - \frac{y^2}{9} = 1$,where $\theta$ is the parameter in its parametric form,then $2 x_1 + 9 \sin^2 \theta = $

The eccentricity of a rectangular hyperbola is

Let $P(a \sec \theta, b \tan \theta)$ and $Q(a \sec \phi, b \tan \phi)$ where $\theta + \phi = \frac{\pi}{2}$ be two points 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 drawn at $P$ and $Q$,then $k=$

For the variable $t,$ the locus of the points of intersection of lines $x-2y=t$ and $x+2y=\frac{1}{t}$ is