If the parabola $x^{2} = 4ay$ passes through the point $(2, 1)$,then the length of the latus rectum is

If the normal chord drawn at $(2 a, 2 a \sqrt{2})$ on the parabola $y^2=4 a x$ subtends an angle $\theta$ at its vertex,then $\theta=$ (in $^{\circ}$)

Find the length of the chord of the parabola $y^2 = 4ax$ which passes through the vertex and makes an angle $\theta$ with the $x-$axis.

The focal distance of a point on the parabola $y^{2}=16x$ whose ordinate is twice the abscissa,is

If the vertex of the conic $y^{2}-4y=4x-4a$ always lies between the straight lines $x+y=3$ and $2x+2y-1=0$, then:

The point of intersection of the latus rectum and the axis of the parabola ${y^2} + 4x + 2y - 8 = 0$ is: