The length of the latus rectum of the parabola ${y^2} - 4y - 2x - 8 = 0$ is

What are the parametric equations of the parabola $y^2 = 8x$?

Let $O$ be the vertex and $Q$ be any point on the parabola $x^2=8y$. If the point $P$ divides the line segment $OQ$ internally in the ratio $1:3$, then the locus of $P$ is

If $(0, 4)$ and $(0, 2)$ are the vertex and focus of a parabola respectively,then what is its equation?

If the parabola $x^2=4ay, (a>0)$ makes an intercept of length $\sqrt{40}$ units on the line $y=1+2x$,then $4a=$

$A$ tangent and a normal are drawn at the point $P(2, -4)$ on the parabola $y^{2} = 8x$,which meet the directrix of the parabola at the points $A$ and $B$ respectively. If $Q(a, b)$ is a point such that $AQBP$ is a square,then $2a + b$ is equal to: