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

Suppose $BOAC$ is a rectangle in the $XY$-plane where $O$ is the origin and $A, B$ lie on the parabola $y=x^2$. Then,$C$ must lie on the curve

Find the equation of the normal to the parabola $y^2 = 8x$ at the point $(2, 4)$.

The equation of the normal at the point $\left( \frac{a}{4}, a \right)$ to the parabola $y^2 = 4ax$ is:

The focal distance of a point $P$ on the parabola $y^{2}=12x$ if the ordinate of $P$ is $6$,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 $\frac{1}{\alpha}+\frac{1}{\alpha^{\prime}}=$