The centre of the hyperbola $9x^{2} - 36x - 16y^{2} + 96y - 252 = 0$ is:

The asymptotes of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ form with any tangent to the hyperbola a triangle whose area is $a^2 \tan \lambda$ in magnitude. Then its eccentricity $e$ is:

The equation of the normal to the hyperbola $\frac{x^2}{16} - \frac{y^2}{9} = 1$ at the point $(8, 3\sqrt{3})$ is

Let the foci of a hyperbola be $(1, 14)$ and $(1, -12)$. If it passes through the point $(1, 6)$,then the length of its latus-rectum is:

What is the distance between the directrices of the hyperbola $x = 8 \sec \theta, y = 8 \tan \theta$ (in $\sqrt{2}$)?

The locus of the middle points of the chords of the hyperbola $3x^2 - 2y^2 + 4x - 6y = 0$ parallel to $y = 2x$ is