Conic Sections and Elements of Conic Curves

GeoGebra Commands & Parameters

1. Intersect(yAxis, xAxis) → V
2. Point(zAxis) → B
3. Line(V, B) → a
4. InfiniteCone(V, B, g) → cone
5. Point(a) → H
6. Plane(Q_1, a) → b
7. Rotate(B, p, V, b) → B'
8. Angle(B, V, B', b) → α
9. Line(V, B') → c
10. Line(Q_1, c) → d
11. IntersectPath(b, cone) → e
12. Intersect(a, d) → A
13. Rotate(Q_1, (-p), A, b) → P'
14. Angle(P', A, Q_1, b) → β
15. Rotate(B, g, V, b) → B'_1
16. Angle(B, V, B'_1, b) → γ
17. Intersect(d, e) → V_1, V_2
18. Midpoint(V_2, V_1) → C
19. OrthogonalLine(C, b) → f
20. AngularBisector(V, V_1, A) → i
21. OrthogonalLine(Q_1, e) → h
22. Plane(d, h) → j
23. IntersectPath(j, cone) → k
24. OrthogonalLine(V_1, i, b) → l
25. Intersect(a, i) → E2
26. Intersect(l, a) → E1
27. Line(V, V_1) → m
28. Intersect(f, k) → V_3, V_4
29. Intersect(d, a) → E
30. Line(V, V_1) → b_1
31. AngularBisector(d, m) → n, q
32. Intersect(a, n) → E_1
33. Intersect(a, q) → E_2
34. OrthogonalLine(E_1, m, b) → r
35. OrthogonalLine(E_2, m, b) → s
36. Intersect(m, r) → D
37. Intersect(m, s) → F
38. Circle(a, D) → e_1
39. Circle(a, F) → e_2
40. Sphere(E_1, D) → o
41. Sphere(E_2, F) → u
42. Mirror(D, a) → D'
43. Mirror(F, a) → F'
44. Plane(e_1) → v
45. Plane(e_2) → w
46. IntersectPath(j, v) → d_1
47. IntersectPath(j, w) → d_2
48. OrthogonalLine(E_1, d, b) → k_1
49. OrthogonalLine(E_2, d, b) → l_1
50. Intersect(d, k_1) → F_1
51. Intersect(d, l_1) → F_2
52. Segment(V_3, V_4) → n_1
53. Ray(V_1, F_1) → p_1
54. Ray(V_2, F_2) → q_1
55. Intersect(d, d_1) → G
56. Segment(V_2, V_1) → m_1
57. Tangent(V_1, k) → t_1, i_2
58. Tangent(V_2, k) → j_2, t_7
59. Tangent(V_3, k) → k_2, t_8
60. Tangent(V_4, k) → l_2, t_9
61. Circle(C, F_1, j) → p_2
62. Circle(C, F_2, j) → c_3
63. Intersect(t_7, c_3, 2) → I
64. Line(C, I) → i_1
65. Intersect(t_1, c_3, 1) → J
66. Line(C, J) → t_{10}
67. Point(t_{10}) → K
68. Point(i_1) → L
69. Circle(F_2, Segment[V_1, V_2], j) → c_2
70. Intersect(c_2, k) → O, Z, G_1, J_1
71. Intersect(d, c_2, 1) → T
72. Intersect(d, c_2, 2) → U
73. OrthogonalLine(F_1, d, j) → t_6
74. Intersect(t_6, c_2, 2) → M
75. Intersect(t_6, c_2, 1) → N
76. CircumcircleArc(M, T, N) → e_4
77. CircumcircleArc(M, U, N) → f_2
78. CircumcircleArc(M, T, N) → g_2
79. Point(f_2) → P_1
80. Point(g_2) → R
81. Line(P_1, F_2) → b_2
82. LineBisector(P_1, F_1, j) → h_2
83. Intersect(b_2, h_2) → S
84. Locus(S, P_1) → loc1
85. Line(F_2, R) → m_2
86. LineBisector(F_1, R, j) → n_2
87. Intersect(m_2, n_2) → W
88. Locus(W, R) → loc2
89. Circle(F_1, Radius[c_2], j) → c_1
90. Point(k) → P
91. Segment(P, F_1) → r1
92. OrthogonalLine(P, d_1, j) → s_2
93. Intersect(d_1, s_2) → A_1
94. Segment(P, A_1) → Pd_1
95. Textfield(Q_1) → ct1
96. Line(V, P) → b_3
97. Circle(E, Q_1, b) → g_3
98. Point(g_3) → B_1
99. Rotate(Q_1, (-p), E, b) → Q'
100. Angle(Q', E, Q_1, b) → δ
101. Point(a) → C_1
102. Circle(V, C_1, b) → h_3
103. Rotate(C_1, g, V, b) → D_1
104. Angle(C_1, V, D_1, b) → ε
105. Plane(V, j) → j_3
106. IntersectPath(j_3, cone) → k_3
107. Intersect(d, f) → C_e
108. PointIn(j) → Q
109. Line(Q, f) → a_1
110. Line(Q, d) → f_1
111. Segment(F_1, P) → r_1
112. Segment(P, F_2) → r_2
113. Line(F_2, P) → d_3
114. Point(d_3) → H_1
115. Point(d_3) → I_1
116. Ray(F_2, H_1) → n_3
117. Ray(P, I_1) → m_3
118. Tangent(P, k) → p_3, t
119. Plane(V, E, V_1) → w_3
120. IntersectPath(w_3, j) → f_4
121. OrthogonalLine(P, w_3) → g_4
122. Intersect(f_4, g_4) → K_1
123. Line(V, K_1) → h_4
124. IntersectPath(w_3, j_3) → i_4
125. IntersectPath(w_3, v) → j_4
126. IntersectPath(w_3, w) → k_4
127. Circle(E1, F, w_3) → c_4
128. Circle(E2, D, w_3) → d_4
129. Line(V_2, t_1) → t_2
130. Tangent(P, k) → l_4,
131. Midpoint(F_1, F_2) → C_2
132. Mirror(C_e, t_{10}) → L_1
133. Mirror(t_{10}, d) → t_{11}
134. OrthogonalLine(V_3, t_1, j) → t_3
135. OrthogonalLine(V_4, t_1, j) → t_4
136. Line(V, V_4) → j_1
137. Line(V, V_3) → m_4
138. Line(V, V_2) → n_4
139. Line(V, V_1) → p_4
140. Line(V, d) → q_4
141. Line(V, t_{11}) → a_4
142. Line(V, t_{10}) → b_4