The equation of the hyperbola whose foci are $(-2, 0)$ and $(2, 0)$ and eccentricity is $2$ is given by :-

The foci of the hyperbola $2{x^2} - 3{y^2} = 5$, is

The foci of a hyperbola are $( \pm 2,0)$ and its eccentricity is $\frac{3}{2}$. A tangent, perpendicular to the line $2 x+3 y=6$, is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the $x$ - and $y$-axes are $a$ and $b$ respectively, then $|6 a|+|5 b|$ is equal to $..........$.

Consider a hyperbola $\mathrm{H}$ having centre at the origin and foci and the $\mathrm{x}$-axis. Let $\mathrm{C}_1$ be the circle touching the hyperbola $\mathrm{H}$ and having the centre at the origin. Let $\mathrm{C}_2$ be the circle touching the hyperbola $\mathrm{H}$ at its vertex and having the centre at one of its foci. If areas (in sq. units) of $\mathrm{C}_1$ and $\mathrm{C}_2$ are $36 \pi$ and $4 \pi$, respectively, then the length (in units) of latus rectum of $\mathrm{H}$ is

A hyperbola whose transverse axis is along the major axis of then conic, $\frac{{{x^2}}}{3} + \frac{{{y^2}}}{4} = 4$ and has vertices at the foci of this conic . If the eccentricity of the hyperbola is $\frac{3}{2}$ , then which of the following points does $NOT$ lie on it ?

The eccentricity of curve ${x^2} - {y^2} = 1$ is