If for a hyperbola the ratio of the length of the conjugate axis to the length of the transverse axis is $3:2$,then the ratio of the distance between the foci to the distance between the two directrices is

The equation of the hyperbola referred to its axes as axes of coordinate and whose distance between the foci is $16$ and eccentricity is $\sqrt{2}$ is:

Find the equations of the tangent and normal to the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ at the point $(x_{0}, y_{0})$.

What is the distance between the directrices of the hyperbola $x = 8 \sec \theta, y = 8 \tan \theta$ (in $\sqrt{2}$)?

Let the sum of the focal distances of the point $P(4,3)$ on the hyperbola $H : \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ be $8 \sqrt{\frac{5}{3}}$. If for $H$,the length of the latus rectum is $l$ and the product of the focal distances of the point $P$ is $m$,then $9l^2 + 6m$ is equal to :-

The equation of the pair of asymptotes of the hyperbola $\frac{(x-3)^2}{3}-\frac{(y-2)^2}{2}=1$ is