Tangent from Point not on Parabola
Author: M. Dabbs, R. Walcott

Drag point P.  Move points D and S.

Double click to open independently.

Point of Tangency (1)

Point of Tangency (2)

A = (-3.84, 1.18)
B = (7.72, 1.18)
a = Line(A, B)
D = Point(a)
S = Point(a)
O = Midpoint(D, S)
b = OrthogonalLine(D, a)
F = Point(b)
c = OrthogonalLine(F, b)
d = Segment(F, S)
G = Midpoint(d)
e = OrthogonalLine(G, d)
H = Intersect(c, e)
loc1 = Locus(H, F)
P = (-3.9, 0.68)
f = Segment(P, S)
J = Midpoint(f)
g = Circle(J, P)
h = OrthogonalLine(O, a)
K, L = Intersect(g, h)
i = Line(P, L)
j = Line(P, K)
K' = Dilate(K, 2.0, O)
L' = Dilate(L, 2.0, O)
k = OrthogonalLine(K', h)
l = OrthogonalLine(L', h)
m = Segment(L', L)
n = Segment(L, O)
C = Intersect(l, i)
p = Segment(O, K)
q = Segment(K, K')
I = Intersect(k, j)
o = false
r = false