圆锥曲线 - Dandelin 证明

GeoGebra 命令及参数

1. PointIn(xz) → K
2. Mirror(K, zAxis) → K'
3. Angle(K, O, K') → α
4. Line((-3, 0, 0), (-3, 0, 1) + K) → h_1
5. Point(h_1) → E_3
6. Plane(E_1, E_2, E_3) → ε
7. Line(K, O) → g_1
8. Line(K', O) → g_2
9. InfiniteCone(O, zAxis, α / 2) → a
10. Midpoint(E_1, E_2) → B_1
11. Line(E_3, B_1) → b
12. Intersect(b, g_1) → A
13. Intersect(b, g_2) → B
14. Line(O, (0, 0, 1)) → zA
15. Circle(A, 1, xz) → c
16. Intersect(g_1, c) → C, D
17. Intersect(b, c) → E, F
18. Circle(E, 1, xz) → d
19. Circle(D, 1, xz) → e
20. Intersect(e, d) → G, H, ,
21. Line(A, G) → w_1
22. OrthogonalLine(A, w_1, xz) → w_2
23. Intersect(zA, w_1) → M_1
24. Intersect(zA, w_2) → M_2
25. OrthogonalLine(M_1, g_1, xz) → f
26. OrthogonalLine(M_2, g_1, xz) → g
27. Intersect(g_1, f) → I
28. Intersect(g_1, g) → J
29. Segment(M_1, I) → r_1
30. Segment(M_2, J) → r_2
31. Sphere(M_1, I) → sp1
32. Sphere(M_2, J) → sp2
33. Circle(zA, J) → p
34. Circle(zA, I) → q
35. Point(p) → L
36. Line(L, O) → j
37. Intersect(j, q) → M,
38. Intersect(j, ε) → P
39. IntersectPath(ε, a) → r
40. OrthogonalLine(M_1, b, xz) → l
41. OrthogonalLine(M_2, b, xz) → m
42. Intersect(b, l) → F_1
43. Intersect(b, m) → F_2
44. Segment(L, P) → s_1
45. Segment(P, F_2) → s_2
46. Intersect(j, q, 1) → N
47. Segment(P, N) → t_1
48. Segment(P, F_1) → t_2
49. Circle(M_1, I, xz) → k
50. Circle(M_2, J, xz) → s