雙曲線的第二定義
Author: 藍邦偉  老師

雙曲線的第二定義：

雙曲線的離心率: 

\overline{PF}=e·d(P,L)

雙曲線的一條準線:

移動d決定準線

移動e決定離心率

Reset

Start

d = 4 (slider from 1 to 5, step 0.1)
e = 3 (slider from 1.1 to 10, step 0.1)
θ = 0 rad (slider from 1.5707963267948966 to 4.71238898038469, step 0.1*°)
F = (0, 0)
P: (e * d / (1 - e * cos(θ)); θ)
a = CurveCartesian(e * d / (1 - e * cos(θ)) * cos(θ), e * d / (1 - e * cos(θ)) * sin(θ), θ, 0, 6.283185307179586)
L: x = -d
b = OrthogonalLine(P, L)
B = Intersect(b, L)
c = Segment(P, F)
f = Segment(B, P)
B_1: (x(Corner[1]), 0)
B_2: (x(Corner[2]), 0)
B_3: (0, y(Corner[2]))
B_4: (0, y(Corner[3]))
u = Vector(B_1, B_2)
v = Vector(B_3, B_4)
T_1 = Corner(1)
T_4 = Corner(4)
T_2: (3.1 * Corner[1] + 0.9 * Corner[2]) / 4
T_3: (3.1 * Corner[4] + 0.9 * Corner[3]) / 4
g = Segment(T_2, T_3)
多邊形1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
text2: "L:x=" + d
text3: "e=\frac{c}{a}=\frac{" + (LaTeX[c]) + "}{" + (LaTeX[f]) + "}=" + (LaTeX[e]) + ""