What is the length of the latus rectum of the parabola $x^2 - 4x - 8y + 12 = 0$?

The intercepts of the focal chord (which is a part of the latus rectum) to the parabola $y^{2}=4ax$ are $b$ and $k$. Then $k$ is equal to:

What is the vertex of the parabola $y^2 + 6x - 2y + 13 = 0$?

The length of the focal chord of the parabola $y^2 = 4ax$ at a distance $p$ from the vertex is:

Let $M$ be the foot of the perpendicular from a point $P$ on the parabola $y^2=8(x-3)$ onto its directrix and let $S$ be the focus of the parabola. If $\triangle SPM$ is an equilateral triangle,then $P$ is equal to

Let $P$ be a point on the parabola $y^2 = 4ax$,where $a > 0$. The normal to the parabola at $P$ meets the $x$-axis at a point $Q$. The area of the triangle $PFQ$,where $F$ is the focus of the parabola,is $120$. If the slope $m$ of the normal and $a$ are both positive integers,then the pair $(a, m)$ is