The latus rectum of the hyperbola $9{x^2} - 16{y^2} - 18x - 32y - 151 = 0$ is
$\frac{9}{4}$
$9$
$\frac{3}{2}$
$\frac{9}{2}$
The eccentricity of a hyperbola passing through the points $(3, 0)$, $(3\sqrt 2 ,\;2)$ will be
If $5{x^2} + \lambda {y^2} = 20$ represents a rectangular hyperbola, then $\lambda $ equals
If the foci of a hyperbola are same as that of the ellipse $\frac{x^2}{9}+\frac{y^2}{25}=1$ and the eccentricity of the hyperbola is $\frac{15}{8}$ times the eccentricity of the ellipse, then the smaller focal distance of the point $\left(\sqrt{2}, \frac{14}{3} \sqrt{\frac{2}{5}}\right)$ on the hyperbola, is equal to
What will be equation of that chord of hyperbola $25{x^2} - 16{y^2} = 400$, whose mid point is $(5, 3)$
Find the coordinates of the foci and the vertices, the eccentricity,the length of the latus rectum of the hyperbolas : $y^{2}-16 x^{2}=16$