The area of the triangle formed by the lines joining the vertex of the parabola $x^2 = 12y$ to the ends of its latus rectum is .................. $sq. \ unit$.

Let $(x, y)$ be any point on the parabola $y^2 = 4x$. Let $P$ be the point that divides the line segment from $(0, 0)$ to $(x, y)$ in the ratio $1:3$. Then the locus of $P$ is

Let the tangent and normal at any point $P(at^2, 2at)$, $(a > 0)$, on the parabola $y^2 = 4ax$ meet the axis of the parabola at $T$ and $G$ respectively. Then the radius of the circle through $P, T$ and $G$ is

If $y=mx+1$ is a tangent to the parabola $y^2=4x$,then $m=$

$A$ set of parallel chords of the parabola $y^2 = 4ax$ have their mid-points on:

The acute angle between the tangents drawn at the point of intersection (other than the origin) of the curves $x^2=4y$ and $y^2=4x$ is