Parabola with Focus and Directrix
Author: M. Dabbs, R. Walcott

Drag point P.  Move points D0 and S.

Double click to open independently

 \frac{SP}{PD} = e = 1

 D_0O = OS

Properties

Tangent

A = (-0.96, 0.98)
B = (9.82, 0.98)
a = Line(A, B)
D_0 = Point(a)
b = OrthogonalLine(D_0, a)
S = Point(a)
E = Point(b)
c = Segment(E, S)
F = Midpoint(E, S)
d = OrthogonalLine(F, c)
e = OrthogonalLine(E, b)
G = Intersect(d, e)
loc1 = Locus(G, E)
P = Point(loc1)
f = Circle(P, S)
g = OrthogonalLine(P, b)
D = Intersect(b, g)
h = Segment(D, P)
i = Segment(P, S)
j = Segment(D, S)
J = Midpoint(D, S)
k = Line(P, J)
α = Angle(P, J, D)
O = Midpoint(D_0, S)
l = OrthogonalLine(O, a)
m = false
n = false