The product of the lengths of the perpendiculars from any point on the hyperbola $x^2-y^2=16$ to its asymptotes is

The directrix of the hyperbola $\frac{x^2}{9} - \frac{y^2}{4} = 1$ is:

If $y=x+\sqrt{2}$ is a tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{2}=1$,then the equations of its directrices are

Let $P$ be the foot of the perpendicular from the focus $S$ of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ on the line $bx-ay=0$ and let $C$ be the centre of the hyperbola. Then, the area of the rectangle whose sides are equal to $SP$ and $CP$ is

What is the area of the triangle formed by the lines $x - y = 0$,$x + y = 0$,and any tangent to the hyperbola $x^{2} - y^{2} = a^{2}$?

Find the equation of the hyperbola satisfying the given conditions: Foci $(\pm 3 \sqrt{5}, 0)$,the latus rectum is of length $8$.