The distance between the directrices of a rectangular hyperbola is $10$ units, then distance between its foci is
$10\sqrt 2 $
$5$
$5\sqrt 2 $
$20$
The equation of the tangents to the hyperbola $3{x^2} - 4{y^2} = 12$ which cuts equal intercepts from the axes, are
The locus of the centroid of the triangle formed by any point $\mathrm{P}$ on the hyperbola $16 \mathrm{x}^{2}-9 \mathrm{y}^{2}+$ $32 x+36 y-164=0$, and its foci is:
If $(a -2)x^2 + ay^2 = 4$ represents rectangular hyperbola, then $a$ equals :-
Which of the following equations in parametric form can represent a hyperbola, where $'t'$ is a parameter.
If $ PN$ is the perpendicular from a point on a rectangular hyperbola $x^2 - y^2 = a^2 $ on any of its asymptotes, then the locus of the mid point of $PN$ is :