If $A$ and $B$ are two points in a plane,such that $|PA - PB| = \text{constant}$,then the locus of $P$ is

The line $3x - 4y = 5$ is a tangent to the hyperbola $x^2 - 4y^2 = 5$. The point of contact is

If $e$ and $e'$ are the eccentricities of a hyperbola and its conjugate hyperbola respectively,then $\frac{1}{e^2} + \frac{1}{e'^2} = \dots$

The length of the latus rectum of the hyperbola $\frac{x^2}{\cos^2 \alpha} - \frac{y^2}{\sin^2 \alpha} = 4$ is (where $\alpha \neq \frac{n\pi}{2}, n \in I$).

The locus of the midpoint of the system of parallel chords parallel to the line $y = 2x$ for the hyperbola $9x^2 - 4y^2 = 36$ is

Find the length of the latus rectum of the hyperbola $16x^2 - 9y^2 = 144$. (in $/3$)