The distance of the focus of the parabola $y^2 = 16x$ from its directrix is...

One of the points on the parabola $y^2 = 12x$ with focal distance $12$ is:

Let $O$ be the origin and $A$ be a point on the curve $y^2=4x$. Then the locus of the midpoint of $OA$ is:

Find the vertex of the parabola $y^2 + 6x - 2y + 13 = 0$.

If the focus of a parabola is $(3, 0)$ and the length of its latus rectum is $8$,what is its vertex?

Let $a, r, s, t$ be nonzero real numbers. Let $P(at^2, 2at)$,$Q(at'^2, 2at')$,$R(ar^2, 2ar)$,and $S(as^2, 2as)$ be distinct points on the parabola $y^2=4ax$. Suppose that $PQ$ is the focal chord and lines $QR$ and $PK$ are parallel,where $K$ is the point $(2a, 0)$.
$1.$ The value of $r$ is
$(A) -\frac{1}{t}$ $(B) \frac{t^2+1}{t}$ $(C) \frac{1}{t}$ $(D) \frac{t^2-1}{t}$
$2.$ If $st=1$,then the tangent at $P$ and the normal at $S$ to the parabola meet at a point whose ordinate is
$(A) \frac{(t^2+1)^2}{2t^3}$ $(B) \frac{a(t^2+1)^2}{2t^3}$ $(C) \frac{a(t^2+1)^2}{t^3}$ $(D) \frac{a(t^2+2)^2}{t^3}$
Give the answer for question $1$ and $2$.