Subtangent and subnormal of parabola
Author: Daniela Velichová

Subtangent of parabola is the line segment RO, 
where R is the intersection point of parabola axis o 
and parabola tangent line t in the arbitrary point T,
and O is the intersection point of parabola axis o 
and line k perpendicular to o through the point T.

Parabola vertex V is the centre of subtangent RO.

Subnormal of parabola is the line segment ON,
where N is the intersection point of parabola axis o
and parabola normal n, perpendicular to the parabola
tangent line t in the arbitrary point T.

Focus of parabola F is the centre of line segment RN,
which is the sum of parabola subtangent and subnormal.




Move the point T along the parabola c.

F = (6.82, -2.04)
B = (0.5066666666666642, 10.196666666666669)
C = (0.3866666666666641, -9.963333333333335)
d = Line(B, C)
o = OrthogonalLine(F, d)
c = Parabola(F, d)
V = Intersect(c, o)
T = Point(c)
t = Tangent(T, c)
R = Intersect(t, o)
k = OrthogonalLine(T, o)
O = Intersect(o, k)
n = OrthogonalLine(T, t)
N = Intersect(n, o)