$A$ parabola passing through the point $(-4, -2)$ has its vertex at the origin and the $y$-axis as its axis. The length of the latus rectum of the parabola is:

Find the measure of the angle in degrees subtended by the double ordinate of the parabola $y^2 = 4ax$ at its vertex.

What is the focus of the parabola $4y^2 + 12x - 20y + 67 = 0$?

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

For the parabola $y^2 = 8(x - 3)$,let $P$ be a point on it. Let $M$ be the foot of the perpendicular from $P$ to the directrix,and $S$ be the focus of the parabola. If $\triangle SPM$ is an equilateral triangle,find the length of each side of the triangle.

At what points does the line $2x + y - 1 = 0$ intersect the parabola $y^2 = 4x$?