If transverse and conjugate axes of a hyperbola are equal, then its eccentricity is
$\sqrt 3 $
$\sqrt 2 $
$1/\sqrt 2 $
$2$
Eccentricity of the curve ${x^2} - {y^2} = {a^2}$ is
The vertices of a hyperbola $H$ are $(\pm 6,0)$ and its eccentricity is $\frac{\sqrt{5}}{2}$. Let $N$ be the normal to $H$ at a point in the first quadrant and parallel to the line $\sqrt{2} x + y =2 \sqrt{2}$. If $d$ is the length of the line segment of $N$ between $H$ and the $y$-axis then $d ^2$ is equal to $............$.
A tangent to the hyperbola $\frac{{{x^2}}}{4} - \frac{{{y^2}}}{2} = 1$ meets $x-$ axis at $P$ and $y-$ axis at $Q$. Lines $PR$ and $QR$ are drawn such that $OPRQ$ is a rectangle (where $O$ is the origin). Then $R$ lies on
The number of possible tangents which can be drawn to the curve $4x^2 - 9y^2 = 36$ , which are perpendicular to the straight line $5x + 2y -10 = 0$ is
Find the equation of the hyperbola satisfying the give conditions: Foci $(0, \,\pm \sqrt{10}),$ passing through $(2,\,3)$