If the vertex of a parabola is at the origin and the directrix is $x + 5 = 0$,then its latus rectum is

Let $S$ be the focus of the parabola $y^2=4ax$ and $PQ$ be a focal chord such that $SP=\alpha$ and $SQ=\alpha^{\prime}$. Then $\frac{1}{\alpha}+\frac{1}{\alpha^{\prime}}=$

$A$ beam of light travels along the line $y = -4$ from right to left and strikes a parabola at point $P$. If the focus and directrix of the parabola are $(2, 0)$ and $x = -2$ respectively,then find the coordinates of the point where the reflected beam contacts the parabola again.

If two tangents drawn from a point $P$ to the parabola $y^{2}=16(x-3)$ are at right angles,then the locus of point $P$ is :

What is the equation of the normal to the curve $y^2 = 16x$ at the point $(1, 4)$?

If a perpendicular drawn through the vertex $O$ of the parabola $y^2=4ax$ to any of its tangent meets the tangent at $N$ and the parabola at $M$,then $ON \cdot OM=$