Find the parameter $t$ for the point $(4, -6)$ on the parabola $y^2 = 9x$.

The equation of the directrix of the parabola $3x^{2} = 16y$ is

Let $PQ$ be a focal chord of the parabola $y^2=4ax$. The tangents to the parabola at $P$ and $Q$ meet at a point $R$ lying on the line $y=2x+a$,where $a > 0$.
$1.$ The length of the chord $PQ$ is:
$(A)$ $7a$ $(B)$ $5a$ $(C)$ $2a$ $(D)$ $3a$
$2.$ If the chord $PQ$ subtends an angle $\theta$ at the vertex of the parabola $y^2=4ax$,then $\tan \theta$ is:
$(A)$ $\frac{2}{3}\sqrt{7}$ $(B)$ $\frac{-2}{3}\sqrt{7}$ $(C)$ $\frac{2}{3}\sqrt{5}$ $(D)$ $\frac{-2}{3}\sqrt{5}$

The equation of the locus of all points equidistant from the point $(4, 2)$ and the $x$-axis is:

What is the equation of the directrix of the parabola $x^2 = -ay$?

Let the tangent and normal at any point $P(at^2, 2at)$,$(a > 0)$,on the parabola $y^2 = 4ax$ meet the axis of the parabola at $T$ and $G$ respectively. Then the radius of the circle through $P, T$ and $G$ is