The parametric equations of the curve $y^2 = 8x$ are

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

The points $(at_1^2, 2at_1)$,$(at_2^2, 2at_2)$,and $(a, 0)$ will be collinear,if

If $(2,3)$ is the focus and $x-y+3=0$ is the directrix of a parabola,then the equation of the tangent drawn at the vertex of the parabola is

If two tangents to the parabola $y^2=8x$ meet the tangent at its vertex in $M$ and $N$ such that $MN=4$,then the locus of the point of intersection of those two tangents is

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