If angle between asymptotes of hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{3} = 4$ is $\frac {\pi }{3}$ , then its conjugate hyperbola is
$\frac{{{y^2}}}{{12}} - \frac{{{x^2}}}{9} = 1$
$\frac{{{y^2}}}{{12}} - \frac{{{x^2}}}{{25}} = 1$
$\frac{{{y^2}}}{{12}} - \frac{{{x^2}}}{{36}} = 1$
$\frac{{{y^2}}}{{12}} - \frac{{{x^2}}}{4} = 1$
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
Centre of hyperbola $9{x^2} - 16{y^2} + 18x + 32y - 151 = 0$ is
If the eccentricities of the hyperbolas $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ and $\frac{{{y^2}}}{{{b^2}}} - \frac{{{x^2}}}{{{a^2}}} = 1$ be e and ${e_1}$, then $\frac{1}{{{e^2}}} + \frac{1}{{e_1^2}} = $
The eccentricity of a hyperbola passing through the points $(3, 0)$, $(3\sqrt 2 ,\;2)$ will be