If the tangents at $P$ and $Q$ on a parabola meet at $T$,then $SP, ST$ and $SQ$ are in

The locus of the midpoint of the chord of the parabola $y^2 = 4ax$ which subtends a right angle at the vertex is

Let $S$ be the set of all $a \in \mathbb{N}$ such that the area of the triangle formed by the tangent at the point $P(b, c)$,where $b, c \in \mathbb{N}$,on the parabola $y^2 = 2ax$ and the lines $x = b$ and $y = 0$ is $16 \text{ unit}^2$. Then $\sum_{a \in S} a$ is equal to $..........$.

The locus of a point which divides the line segment joining the focus and any point on the parabola $y^2 = 12x$ in the ratio $m:n$ $(m+n \neq 0)$ is a parabola. Then the length of the latus rectum of that parabola is

What is the angle subtended by the latus rectum of the parabola $y^2 = ax$ at its vertex?

The length of the chord of the parabola $y^2 = 4ax$ which passes through the vertex and makes an angle $\theta$ with the axis of the parabola is: