If the vertices of a hyperbola be at $(-2, 0)$ and $(2, 0)$ and one of its foci be at $(-3, 0)$, then which one of the following points does not lie on this hyperbola?
$\left( { - 6 , 2\sqrt {10} } \right)$
$\left( {2\sqrt 6 , 5} \right)$
$\left( { 4 , \sqrt {15} } \right)$
$\left( { 6 , 5\sqrt {2} } \right)$
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola $16 x^{2}-9 y^{2}=576$
Find the equation of the hyperbola where foci are $(0,\,±12)$ and the length of the latus rectum is $36.$
If the eccentricity of the hyperbola $x^2 - y^2 \sec^2 \alpha = 5$ is $\sqrt 3 $ times the eccentricity of the ellipse $x^2 \sec^2 \alpha + y^2 = 25, $ then a value of $\alpha$ is :
The distance between the directrices of a rectangular hyperbola is $10$ units, then distance between its foci is
The condition that the straight line $lx + my = n$ may be a normal to the hyperbola ${b^2}{x^2} - {a^2}{y^2} = {a^2}{b^2}$ is given by