The axis of a parabola is along the line $y=x$ and the distance of its vertex $A$ from $(0,0)$ is $\sqrt{2}$ and that of its focus $S$ from $(0,0)$ is $2 \sqrt{2}$. If $A$ and $S$ lie in first quadrant, then the equation of the parabola in parametric form is

If $y^2=16 x$ is the given parabola, then the point of intersection of the focal chord through the point $(2,2)$ and the double ordinate of length 24 is

Let $P Q$ and $R T$ be two focal chords of the parabola $y^2=16 x$. If $P=(4,8)$ are $R=(16,16)$, then $Q T=$

If $P Q$ is a focal chord of the parabola $y^2=4 x$ with focus $S$ and $P=(4,4)$, then $S Q=$