The common tangent to the parabolas $y^2=32x$ and $x^2=256y$ is:

The axis of the parabola $9y^2 - 16x - 12y - 57 = 0$ is

Consider the parabola $y^2=4x$. Let $S$ be the focus of the parabola. $A$ pair of tangents drawn to the parabola from the point $P=(-2,1)$ meet the parabola at $P_1$ and $P_2$. Let $Q_1$ and $Q_2$ be points on the lines $SP_1$ and $SP_2$ respectively such that $PQ_1$ is perpendicular to $SP_1$ and $PQ_2$ is perpendicular to $SP_2$. Then,which of the following is/are $TRUE$?
$(A)$ $SQ_1=2$
$(B)$ $Q_1Q_2=\frac{3\sqrt{10}}{5}$
$(C)$ $PQ_1=3$
$(D)$ $SQ_2=1$

$A$ normal chord of the parabola $y^2 = 4x$ subtending a right angle at the vertex makes an acute angle $\theta$ with the $x$-axis. Then $\theta$ is equal to:

The line $y = mx + c$ touches the parabola $y^2 = 4a(x + a)$ if...

The angle between the tangents drawn at the end points of the latus rectum of the parabola $y^2 = 4ax$ is