If in a hyperbola,the distance between the foci is $10$ and the transverse axis has length $8$,then the length of its latus rectum is

If $P(\frac{\pi}{6})$ is a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$,$S$ and $S^{\prime}$ are its foci,and $SP + S^{\prime}P - 2|SP - S^{\prime}P| = 0$,then the eccentricity $e$ is:

If the straight line $x \cos \alpha + y \sin \alpha = p$ is a tangent to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,then:

The foci of the hyperbola $4x^2 - 9y^2 - 36 = 0$ are:

If the line $\alpha x+2y=1$, where $\alpha \in \mathbb{R}$, does not meet the hyperbola $x^{2}-9y^{2}=9$, then a possible value of $\alpha$ is:

If a hyperbola passes through the point $P(10, 16)$ and it has vertices at $(\pm 6, 0)$,then the equation of the normal to it at $P$ is