The tangent drawn at any point $P$ to the parabola ${y^2} = 4ax$ meets the directrix at the point $K$. Then the angle which $KP$ subtends at its focus is ............. $^\circ$.

If the line $2x + 3y + n = 0$ is a tangent to the parabola $y^2 = 8x$,then the equation of the normal drawn at the point $(2n, 4\sqrt{n})$ to the parabola $y^2 = 8x$ is

If $P$ is a point which divides the line segment joining the focus of the parabola $y^2=12x$ and a point on the parabola in the ratio $1:2$,then the locus of $P$ is:

Let one end of a focal chord of the parabola $y^{2}=16x$ be $(16, 16)$. If $P(\alpha, \beta)$ divides this focal chord internally in the ratio $5 : 2$, then the minimum value of $\alpha+\beta$ is equal to:

An equilateral triangle is inscribed in the parabola $y^{2}=4ax$,where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

$A$ set of parallel chords of the parabola $y^2 = 4ax$ have their mid-points on: