The parametric equations $x - 2 = t^2$ and $y = 2t$ represent which parabola?

The normal at the point $(2, 4)$ to the parabola $y^2 = 4ax$ meets the parabola again at another point. Find the coordinates of this point.

Find the equation of the normal to the parabola $y^2 = 16x$ having a slope of $-1/4$.

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

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

The value of $\lambda$ for which the curve $(7x+5)^{2}+(7y+3)^{2}=\lambda^{2}(4x+3y-24)^{2}$ represents a parabola is