On a coordinate plane, a parabola opens upwards. The focus is at point (0, p), Point P on the parabola is at (x, y), and point Q on the directrix is (x, negative p). The equation of the directrix line is y = negative p. When the focus and directrix are used to derive the equation of a parabola, two distances were set equal to each other. = StartRoot (x minus x) squared + (y minus (negative p)) squared EndRoot = StartRoot (x minus 0) squared + (y minus p) squared EndRoot The distance between the directrix and is set equal to the distance between the and the same point on the parabola.