Derive the definition of an ellipse from a cone

GeoGebra Commands & Parameters

1. Intersect(xAxis, yAxis) → A
2. Circle(A, B) → c
3. Cone(c, 4) → a_2, d, b
4. PointIn(b) → C
5. PointIn(b) → D
6. PointIn(b) → E
7. Plane(C, D, E) → e
8. IntersectPath(e, b) → f
9. Point(c) → F
10. Plane(F, A, B) → g
11. Point(d) → H
12. Rotate(B, a°, A) → G
13. Segment(H, G) → m
14. Segment(H, A) → n
15. OrthogonalLine(H, e) → p
16. Intersect(p, e) → I
17. Intersect(n, e) → J
18. Plane(H, J, I) → o
19. IntersectPath(e, o) → q
20. Intersect(q, f, 2) → K
21. Intersect(q, f, 1) → L
22. Line(K, H) → r
23. OrthogonalLine(K, o) → s
24. Circle(s, H) → t
25. Intersect(q, t, 1) → M
26. Intersect(r, t, 2) → N
27. Midpoint(M, H) → O
28. Midpoint(N, M) → P
29. Intersect(s, f, 1) → Q
30. Line(K, O) → a_1
31. Intersect(s, f, 1) → R
32. Line(K, P) → b_{13}
33. Intersect(a_1, n) → S
34. Intersect(n, b_{13}) → T
35. OrthogonalLine(S, e) → c_1
36. OrthogonalLine(T, e) → d_1
37. Intersect(c_1, e) → U
38. Intersect(d_1, e) → V
39. Sphere(T, V) → u
40. Sphere(S, U) → v
41. OrthogonalLine(S, m, space) → f_1
42. Intersect(f_1, m) → W
43. Plane(W, g) → g_1
44. IntersectPath(g_1, a_2) → h_1
45. OrthogonalLine(T, m, space) → j_1
46. Intersect(j_1, m) → Z
47. Plane(Z, g) → k_1
48. Rotate(B, a°, A) → B'
49. Angle(B, A, B') → α
50. IntersectPath(k_1, a_2) → p_1
51. Intersect(m, f, 1) → A_1
52. Point(f) → B_1
53. Segment(W, A_1) → m_1
54. Segment(A_1, U) → n_1
55. Segment(Z, A_1) → q_1
56. Segment(A_1, V) → r_1