From the point $(-1, 2)$, tangents are drawn to the parabola $y^2 = 4x$. The area of the triangle formed by the chord of contact and the tangents is: (in $\sqrt{2}$)

Suppose the parabola $(y-k)^2 = 4a(x-h)$ has vertex $A$ and passes through $O = (0,0)$ and $L = (0,2)$. Let $D$ be an end point of the latus rectum. Let the $Y$-axis intersect the axis of the parabola at $P$. Then,$\angle PDA$ is equal to

The position of a moving point in the $XY$-plane at time $t$ is given by $\left( (u \cos \alpha)t, (u \sin \alpha)t - \frac{1}{2}gt^2 \right)$,where $u, \alpha, g$ are constants. The locus of the moving point is

The line $x \cos \alpha + y \sin \alpha = p$ will touch the parabola $y^2 = 4a(x + a)$ if:

The locus of the point of intersection of the perpendicular tangents to the parabola $x^2 = 4ay$ is

The length of the latus rectum of the parabola ${y^2} = 5x + 4y + 1$ is