The equation of the parabola with $(-3, 0)$ as focus and $x + 5 = 0$ as directrix is

Let the locus of the mid-point of the chord through the origin $O$ of the parabola $y^{2}=4x$ be the curve $S$. Let $P$ be any point on $S$. Then the locus of the point, which internally divides $OP$ in the ratio $3:1$, is:

What is the point of intersection of the latus rectum and the axis of the parabola $y^2 - 4y - 2x - 8 = 0$?

The points of contact $Q$ and $R$ of the tangents drawn from the point $P(2, 3)$ to the parabola $y^2 = 4x$ are

Three normals are drawn from the point $(3, 0)$ to the parabola $y^2 = 4x$,meeting the parabola at points $P, Q,$ and $R$. Match the following:

Column-$I$	Column-$II$
$(A)$ Circumradius of $\Delta PQR$	$(P)$ $5/2$
$(B)$ Area of $\Delta PQR$	$(Q)$ $(5/2, 0)$
$(C)$ Centroid of $\Delta PQR$	$(R)$ $(2/3, 0)$
$(D)$ Circumcenter of $\Delta PQR$	$(S)$ $2$

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