[color=#000000][b]Definition of a parabola: [/b][/color][br][br]A parabola is a[color=#ff00ff][b] locus (set of points that meet a certain condition) in a plane, each of which is equidistant form a fixed point [/b][/color](called the focus-point [i]F[/i]) [color=#ff00ff][b]and a given line[/b][/color] (the line that passes through [i]A[/i] and [i]B[/i]) called the directrix. [br][br]Since p is the perpendicular bisector of the segment with endpoints [i]F[/i] and [i]C[/i], every point on [i]p[/i] is equidistant from [i]F[/i] and [i]C[/i]. [br][br]Thus, the [color=#ff00ff][b]pink point[/b][/color] is equidistant from the directrix (line [i]AB[/i]) and the focus ([i]F[/i]). [color=#ff00ff][b]All traces of these pink points form a parabola. [/b][/color][br]