If the line $y\, = \,mx\, + \,7\sqrt 3 $ is normal to the hyperbola $\frac{{{x^2}}}{{24}} - \frac{{{y^2}}}{{18}} = 1,$ then a value of $m$ is
If $(a -2)x^2 + ay^2 = 4$ represents rectangular hyperbola, then $a$ equals :-
Find the equation of the hyperbola satisfying the give conditions: Vertices $(0,\,\pm 3),$ foci $(0,\,±5)$
If the straight line $x\cos \alpha + y\sin \alpha = p$ be a tangent to the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$, then
The equation of the transverse and conjugate axis of the hyperbola $16{x^2} - {y^2} + 64x + 4y + 44 = 0$ are