If the latusrectum of a hyperbola subtends an angle of $120^{\circ}$ at its centre, then its eccentricity is

Let $P\left(\frac{\pi}{4}\right), Q\left(\frac{5 \pi}{4}\right), R\left(\frac{3 \pi}{4}\right), T\left(\frac{7 \pi}{4}\right)$ be the points on the hyperbola $x^2-4 y^2-4=0$ in the parametric form. Then the area of the quadrilateral $P Q R T$ is (in square units)

If $A(1,2,3), B(2,-3,1), C(3,2,-1)$ are three vertices of a tetrahedron $A B C D$ and $G\left(\frac{5}{2}, \frac{3}{2}, \frac{9}{4}\right)$ is its centroid, then the point which divides $G D$ in the ratio $1: 2$ is

Let $D$ be the foot of the perpendicular drawn from the point $A(2,0,3)$ to the line joining the points $B(0,4,1)$ and $C(-2,0,4)$. Then, the ratio in which $D$ divides $B C$ is