Parabola

The parabola make the locus of all points in a plane that are the same distance from a line(directrix) in the plane as from a fixed point(focus) in the plane.
Point Focus = Point Directrix
PF = PD
The parabola has one axis of symmetry, which intersects the parabola at its vertex | p |
The distance from the vertex to the focus is | p |.
The distance from the directrix to the vertex is also | p |.

The General Form of the Equation of a Parabola with Vertex (0, 0)

The parabola equation with vertex (0, 0) and focus on the x-axis is y² = 4px.
The coordinates of the focus are (p, 0).
The equation of the directrix is x = -p.

If p > 0, the parabola opens right.

If p <>, the parabola opens left.

The parabola equation with vertex (0, 0) and focus on the y-axis is x² = 4py.

The coordinates of the focus are (0, p).
The equation of the directrix is y = -p.

If p > 0, the parabola opens up.

If p <> the parabola opens down.