Focus of the parabola ${(y - 2)^2} = 20(x + 3)$ is

The locus of the poles of focal chords of the parabola $y^2 = 4ax$ is

Let $P$ and $Q$ be distinct points on the parabola $y^2=2x$ such that a circle with $PQ$ as diameter passes through the vertex $O$ of the parabola. If $P$ lies in the first quadrant and the area of the triangle $\Delta OPQ$ is $3\sqrt{2}$,then which of the following is (are) the coordinates of $P$?
$(A)$ $(4, 2\sqrt{2})$
$(B)$ $(9, 3\sqrt{2})$
$(C)$ $(\frac{1}{4}, \frac{1}{\sqrt{2}})$
$(D)$ $(1, \sqrt{2})$

$x - 2 = t^2$ and $y = 2t$ are the parametric equations of which parabola?

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

Let $PQ$ be a chord of the parabola $y^2=12x$ and the midpoint of $PQ$ be at $(4,1)$. Then,which of the following points lies on the line passing through the points $P$ and $Q$?