Deriving Hyperbola Definition from a Cone

GeoGebra Commands & Parameters

1. Point(yAxis) → E_1
2. Intersect(xAxis, yAxis) → D_1
3. Point(yAxis) → C_1
4. Line(E_1, C_1) → e_2
5. Point(e_2) → C
6. Circle(E_1, 2, e_2) → f_2
7. Cone(f_2, 4) → w_1, g_2, h_2
8. PointIn(h_2) → H_1
9. PointIn(h_2) → G_1
10. PointIn(h_2) → F_1
11. Plane(F_1, G_1, H_1) → i_2
12. OrthogonalLine(C, i_2) → e
13. Intersect(e, i_2) → D
14. Plane(D_1, C, D) → f
15. IntersectPath(i_2, w_1) → k_2
16. Intersect(f, k_2) → A_2, B_2
17. Intersect(xAxis, yAxis) → A
18. Rotate(B, a°, A) → G
19. Rotate(B, a°, A) → B'
20. Angle(B, A, B') → α
21. Line(C_1, E_1) → b_{11}
22. Circle(C_1, 2, b_{11}) → c_2
23. Cone(c_2, 4) → u_1, d_2, v_1
24. Corner(k_2) → I_1, J_1, T, U
25. IntersectPath(i_2, u_1) → q_2
26. Corner(q_2) → M_1, N_1, V, W
27. Line(B_2, A_2) → g
28. Intersect(g, k_2, 1) → E
29. Intersect(g, q_2, 2) → F
30. Line(E, D_1) → h
31. Midpoint(E, D_1) → H
32. Sphere(E, H) → i
33. Intersect(g, i, 1) → I
34. Midpoint(H, I) → J
35. Line(E, J) → j
36. Intersect(j, e_2) → K
37. Line(D_1, F) → m
38. Midpoint(D_1, F) → L
39. Sphere(F, L) → n
40. Intersect(g, n, 2) → M
41. Midpoint(M, L) → N
42. Line(F, N) → p
43. Intersect(e_2, p) → O
44. OrthogonalLine(K, i_2) → q
45. OrthogonalLine(O, i_2) → r
46. Intersect(r, i_2) → P
47. Intersect(q, i_2) → Q
48. Sphere(K, Q) → o
49. Sphere(O, P) → s
50. OrthogonalLine(K, h, space) → t
51. OrthogonalLine(O, h, space) → a_1
52. Intersect(a_1, h) → R
53. Intersect(t, h) → S
54. OrthogonalPlane(R, e_2) → u
55. OrthogonalPlane(S, e_2) → v
56. IntersectPath(u, s) → c_1
57. IntersectPath(v, o) → d_1
58. Point(xAxis) → Z
59. Circle(D_1, Z) → f_1
60. OrthogonalLine(D_1, xOyPlane) → g_1
61. Point(g_1) → A_1
62. Sphere(D_1, A_1) → h_1
63. Intersect(e_2, h_1, 2) → B_1
64. Midpoint(B_1, A_1) → K_1
65. OrthogonalPlane(D_1, e_2) → i_1
66. IntersectPath(xOyPlane, i_1) → j_1
67. Intersect(j_1, f_1, 2) → L_1
68. Plane(L_1, D_1, K_1) → k_1
69. Point(f_1) → O_1
70. Rotate(O_1, a°, D_1) → P_1
71. Angle(O_1, D_1, P_1) → β
72. OrthogonalLine(P_1, xOyPlane) → m_1
73. Intersect(m_1, k_1) → Q_1
74. OrthogonalLine(Q_1, i_1) → n_1
75. Intersect(n_1, i_1) → R_1
76. Intersect(n_1, h_2, 2) → S_1
77. Line(D_1, S_1) → p_1
78. Intersect(p_1, k_2, 1) → T_1
79. Segment(T_1, P) → r_1
80. Line(T_1, D_1) → a_2
81. Intersect(r_1, q_2, 2) → U_1
82. Line(D_1, U_1) → j_2
83. Intersect(j_2, c_1, 1) → V_1
84. Intersect(a_2, d_1, 1) → W_1
85. Segment(T_1, Q) → q_1
86. Segment(T_1, P) → l_2
87. Intersect(a_2, c_1, 1) → Z_1
88. Segment(Z_1, T_1) → m_2
89. Segment(T_1, W_1) → n_2
90. IntersectPath(f, i_2) → l_1