The equation of the directrix of the parabola $3x^{2} = 16y$ is

Consider the circle $C: x^2+y^2=4$ and the parabola $P: y^2=8x$. If the set of all values of $\alpha$,for which three chords of the circle $C$ on three distinct lines passing through the point $(\alpha, 0)$ are bisected by the parabola $P$,is the interval $(p, q)$,then $(2q-p)^2$ is equal to.............

Find the length of the tangent drawn from an endpoint of the latus rectum of the parabola $y^2 = 4ax$ to a circle of radius $a$ that touches the parabola at its vertex.

The axis of the parabola $9y^2 - 16x - 12y - 57 = 0$ is

The parametric equations of the parabola $y^2-8x-4y-12=0$ are

The equation of the tangent at $P(-4, -4)$ on the curve $x^{2} = -4y$ is