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

The largest value of $k$ for which the circle $x^2+y^2=k^2$ lies completely in the interior of the parabola $y^2=4x+16$ 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 parabola with the focus $(3,0)$ and the directrix $x+3=0$ is:

The number of normals drawn to the parabola $y^2=4x$ from the point $(1,0)$ is

The smallest value of $x^2 - 3x + 3$ in the interval $(-3, 3/2)$ is