What is the vertex of the parabola $y^2 + 6x - 2y + 13 = 0$?

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:
$(A)$ $\frac{2}{3}\sqrt{7}$ $(B)$ $\frac{-2}{3}\sqrt{7}$ $(C)$ $\frac{2}{3}\sqrt{5}$ $(D)$ $\frac{-2}{3}\sqrt{5}$

From the point $(-1, 2)$,tangent lines are drawn to the parabola $y^2 = 4x$. Find the equation of the chord of contact.

$A$ beam is supported at its ends by supports which are $12 \, m$ apart. Since the load is concentrated at its centre,there is a deflection of $3 \, cm$ at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection $1 \, cm$?

The focus of the parabola $y = 2x^{2} + x$ is

If $x-y-3=0$ is a normal drawn through the point $(5,2)$ to the parabola $y^2=4x$,then the slope of the other normal that can be drawn through the same point to the parabola $y^2=4x$ is