A parabola is the locus of a point P such that its distance from a fixed point (focus F) equals its distance from a fixed line (directrix). For $y^2$ = 4ax: vertex = (0,0), focus = (a,0), directrix: x = -a, axis: y = 0. The eccentricity of every parabola is exactly 1. The parameter 'a' alone determines the shape and size. The vertex is the midpoint of the segment from focus to the foot of directrix perpendicular.