Un-hide asymptotes

Un-hide focus directrix property

t = 6.26 (slider from 0 to 6.26, step 0.1)
a = 1 (slider from 0 to 4, step 0.1)
b = 1 (slider from 0 to 4, step 0.1)
h = CurveCartesian((a * sec(v)), (b * tan(v)), v, 0, t)
a1: y = (b / a * x)
a2: y = ((-(b / a)) * x)
c = false
e: sqrt(b^(2) / a^(2) + 1)
text1: "Eccentricity = " + e + ""
P = Point(h)
directrix: x = a / e
F1: ((a * e), 0)
B = Point({a / e, y(P)})
l1 = Segment(B, P)
l2 = Segment(F1, P)
ratio: l2 / l1
text2: "Length of line BP = " + l1 + ""
text3: "Length of line PF1 = " + l2 + ""
d = false