The line $y = 2x + c$ is a tangent to the parabola $y^2 = 16x$,if $c$ equals

The area (in sq. units) of an equilateral triangle inscribed in the parabola $y^{2}=8x$, with one of its vertices at the vertex of this parabola, is (in $\sqrt{3}$)

The locus of the poles of focal chords of the parabola $y^2 = 4ax$ is

The focus of the parabola $y^2 - x - 2y + 2 = 0$ is

Statement $(A)$: If the normal at the ends of the latus rectum of the parabola $y^2 = 4x$ meet the curve again at $P$ and $P'$,then $PP' = 12$ units.
Reason $(R)$: If the normal at $T_1$ to the parabola $y^2 = 4ax$ meets the parabola again at $T_2$,then $T_2 = -T_1 - \frac{2}{T_1}$.

The point at which the line $y = mx + c$ touches the parabola $y^2 = 4ax$ is