双曲线的反射性质——切线与两焦点的等角特性

GeoGebra 命令及参数

1. Point(a) → F_1
2. Ray(F_1, B) → b
3. Ray(F_1, B) → c
4. Point(b) → F_2
5. Midpoint(F_1, F_2) → D
6. Ray(D, F) → g
7. Point(g) → H
8. Ray(D, F_2) → h
9. Point(h) → I
10. Intersect(i, j) → J
11. Hyperbola(F_1, F_2, J) → d
12. Distance(J, F_2) → e
13. Circle(J, k) → p
14. Segment(F_1, J) → l
15. Segment(J, F_2) → m
16. Intersect(p, l) → E,
17. Intersect(p, m) → G,
18. Tangent(J, d) → n,
19. Intersect(p, n) → K, L
20. CircleSector(J, K, G) → q
21. Angle(K, J, G) → α
22. Dilate(F_2, If[0 < o ≤ 1, 1 - o, 0], J) → C'
23. Dilate(F_1, If[1 < o ≤ 2, 2 - o, 0], J) → A'
24. Segment(F_2, C') → r
25. Segment(F_1, A') → s
26. Rotate(q, If[o > 2, ((-(o - 2)) * α), (-α)], J) → q'
27. CircleArc(J, K, G) → t
28. Segment(H, J) → a_1
29. Segment(I, J) → b_1
30. Ray(D, H) → c_1
31. Ray(D, I) → d_1