The equation to the hyperbola having its eccentricity $2$ and the distance between its foci is $8$
$\frac{{{x^2}}}{{12}} - \frac{{{y^2}}}{4} = 1$
$\frac{{{x^2}}}{4} - \frac{{{y^2}}}{{12}} = 1$
$\frac{{{x^2}}}{8} - \frac{{{y^2}}}{2} = 1$
$\frac{{{x^2}}}{{16}} - \frac{{{y^2}}}{9} = 1$
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 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
The line $2 \mathrm{x}+\mathrm{y}=1$ is tangent to the hyperbola $\frac{\mathrm{x}^2}{\mathrm{a}^2}-\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1$. If this line passes through the point of intersection of the nearest directrix and the $\mathrm{x}$-axis, then the eccentricity of the hyperbola is
The locus of middle points of the chords of the circle $x^2 + y^2 = a^2$ which touch the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ is
The value of m for which $y = mx + 6$ is a tangent to the hyperbola $\frac{{{x^2}}}{{100}} - \frac{{{y^2}}}{{49}} = 1$, is