The locus of the poles of focal chords of a parabola is:

$A$ triangle $ABC$ with area $5a^{2}$ is inscribed in the parabola $y^{2} = 4ax$,where the vertex $A$ is at the vertex of the parabola and $BC$ is a focal chord. Find the length of the focal chord.

If $P(-3, 2)$ is an end point of the focal chord $PQ$ of the parabola $y^2 + 4x + 4y = 0$,then the slope of the normal drawn at $Q$ is

Tangents are drawn at points $(x_i, y_i); i = 1, 2, 3$ lying on the parabola $y = x^2$ to enclose a triangle of area $\Delta$. If $x_1, x_2, x_3$ form an increasing arithmetic progression,where $x_1 = -1$ and $y_3 = 9$,then $\Delta$ is ............. $sq. \, units$.

The angle between the tangents drawn from the origin to the parabola $y^2 = 4a(x - a)$ is ............... $^\circ$.

Let $x+y=k$ be a normal to the parabola $y^2=12x$. If $p$ is the length of the perpendicular from the focus of the parabola onto this normal,then $4k-2p^2$ is equal to