The equation of the latus rectum of the parabola $x^2 + 4x + 2y = 0$ is:

Find the equation of the normal to the parabola $y^2 = 8x$ at the point $(2, 4)$.

An arch is in the form of a parabola with its axis vertical. The arch is $10 \, m$ high and $5 \, m$ wide at the base. How wide is it $2 \, m$ from the vertex of the parabola (in $, m$)?

If $(-1,-1)$ is the focus and $x+y+4=0$ is the directrix of a parabola,then its vertex is

$A$ tangent to the curve $x = a t^{2}, y = 2 a t$ is perpendicular to the $X$-axis. Then the point of contact is:

For the parabola $y = \frac{h^3}{3} x^2 + \frac{h^2}{2} x - h + \frac{3}{4 h^3}$,if the equation of the directrix is $y = k$,then find the ratio $k : h$.