The equation of the hyperbola whose directrix is $x + 2y = 1$, focus $(2, 1)$ and eccentricity $2$ will be

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, and the length of the latus rectum of the hyperbola $\frac{y^{2}}{9}-\frac{x^{2}}{27}=1$

The locus of the centroid of the triangle formed by any point $\mathrm{P}$ on the hyperbola $16 \mathrm{x}^{2}-9 \mathrm{y}^{2}+$ $32 x+36 y-164=0$, and its foci is:

Tangents are drawn to the hyperbola $4{x^2} – {y^2} = 36$ at the points $P$ and $Q.$ If these tangents intersect at the point $T(0,3)$ then the area (in sq. units) of $\Delta PTQ$ is :