Find the equation of the parabola that satisfies the following conditions: Focus $(6, 0)$,directrix $x = -6$.

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

The parametric equations of the parabola $y^2 - 12x - 2y - 11 = 0$ are:

Let $M$ be the foot of the perpendicular from a point $P$ on the parabola $y^2=8(x-3)$ onto its directrix and let $S$ be the focus of the parabola. If $\triangle SPM$ is an equilateral triangle,then $P$ is equal to

What is the common tangent to the parabola $y^{2} = 8ax$ and the circle $x^{2} + y^{2} = 2a^{2}$?

Find the locus of the midpoint of the chord of the parabola $y^2 = 4x$ drawn from the vertex.