The equation of the tangents to the hyperbola $3{x^2} - 4{y^2} = 12$ which cuts equal intercepts from the axes, are
$y + x = \pm 1$
$y - x = \pm 1$
$3x + 4y = \pm 1$
$3x - 4y = \pm 1$
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 :
A line parallel to the straight line $2 x-y=0$ is tangent to the hyperbola $\frac{x^{2}}{4}-\frac{y^{2}}{2}=1$ at the point $\left(x_{1}, y_{1}\right) .$ Then $x_{1}^{2}+5 y_{1}^{2}$ is equal to
For the Hyperbola ${x^2}{\sec ^2}\theta - {y^2}cose{c^2}\theta = 1$ which of the following remains constant when $\theta $ varies $= ?$
The difference of the focal distance of any point on the hyperbola $9{x^2} - 16{y^2} = 144$, is
The equation of the hyperbola referred to the axis as axes of co-ordinate and whose distance between the foci is $16$ and eccentricity is $\sqrt 2 $, is