General Quadratic Equation (Hyperbola): Imaginary Roots

GeoGebra Commands & Parameters

1. Point({F_{2x}, F_{2y}}) → F_{2}
2. Circle(F_{2}, (2 * a)) → c_{2}
3. Line(F_{2}, yAxis) → l_{f2yAxis}
4. Point({F_{1x}, F_{1y}}) → F_{1}
5. Hyperbola(F_{1}, F_{2}, a) → h
6. Center(h) → M
7. Point({0, y(M)}) → M''
8. Point({x(M), 0}) → M'
9. Vector(M', M'') → u
10. Circle(F_{1}, (2 * a)) → c_{1}
11. Intersect(c_{1}, l_{f2yAxis}) → P_{C1}, B
12. LineBisector(B, F_{2}) → t_{2x}
13. Line(F_{1}, B) → l_{f1t2x}
14. Line(F_{1}, P_{C1}) → l_{f1t1x}
15. OrthogonalLine(F_{1}, yAxis) → l_{f1xAxis}
16. Intersect(c_{2}, l_{f1xAxis}) → D, F
17. LineBisector(F_{1}, F) → t_{1y}
18. Intersect(t_{1y}, xAxis) → F'_{11}
19. LineBisector(F_{1}, D) → t_{2y}
20. Intersect(t_{2y}, xAxis) → F'_{21}
21. Line(F_{1}, yAxis) → l_{f1yAxis}
22. Intersect(c_{2}, l_{f1yAxis}) → P_{B1}, A
23. Line(F_{2}, A) → l_{f2t2x}
24. LineBisector(P_{B1}, F_{1}) → t_{1x}
25. Intersect(t_{2y}, t_{1x}) → C
26. Circle(M, C) → o
27. Radius(o) → r
28. Line(F_{2}, P_{B1}) → l_{f2t1x}
29. Angle(l_{f2t1x}, t_{1x}) → α_{2}
30. Angle(l_{f2t1x}, l_{f1t1x}) → α_{1}
31. If(Min[α_{1}, 360° - α_{1}] > Min[α_{2}, 360° - α_{2}], Intersect[l_{f1t2x}, l_{f2t2x}], Intersect[l_{f1t2x}, t_{2x}]) → T_{2x}
32. OrthogonalLine(T_{2x}, xAxis) → t'_{2y}
33. Intersect(o, t'_{2y}) → J, K
34. OrthogonalLine(J, yAxis) → d
35. Intersect(d, yAxis) → F''_{11}
36. Intersect(t'_{2y}, xAxis) → V'_{2}
37. If(Min[α_{1}, 360° - α_{1}] > Min[α_{2}, 360° - α_{2}], Intersect[l_{f1t1x}, l_{f2t1x}], Intersect[l_{f1t1x}, t_{1x}]) → T_{1x}
38. OrthogonalLine(T_{1x}, xAxis) → t'_{1y}
39. Intersect(t'_{1y}, xAxis) → V'_{1}
40. If(Distance[F'_{11}, F'_{21}] > Distance[V'_{1}, V'_{2}], true, false) → h'IsHyperbola
41. If(h'IsEllipse, Intersect[t_{2x}, yAxis]) → V''_{4}
42. If(F_{1x} ≟ F_{2x} ∨ F_{1y} ≟ F_{2y}, Line[M, yAxis], If[h'IsHyperbola, Hyperbola[F'_{11}, F'_{21}, V'_{2}], Ellipse[F'_{11}, F'_{21}, V'_{2}]]) → h'
43. FirstAxisLength(h') → a'
44. If(r > a' ∨ (¬Defined[a']), true, false) → h''MajorAxisIsyAxis
45. SecondAxis(h') → e'_{y}
46. Intersect(h', e'_{y}) → V'_{3}, V'_{4}
47. Semicircle(V'_{4}, V'_{3}) → c_{aux2}
48. Intersect(c_{aux2}, xAxis) → S,
49. If(h'IsHyperbola, Intersect[t_{2x}, yAxis], Translate[S, u]) → V''_{2}
50. If(h'IsHyperbola, Intersect[t_{1x}, yAxis], Mirror[V''_{2}, yAxis]) → V''_{1}
51. Circle(V''_{4}, Distance[M'', V''_{1}]) → c_{aux3}
52. Intersect(c_{aux3}, Line[M'', xAxis]) → F''_{21}, F''_{22}
53. OrthogonalLine(K, yAxis) → s
54. Intersect(s, yAxis) → F''_{12}
55. If(h''MajorAxisIsyAxis, F''_{11}, F''_{21}) → F''_1
56. If(h''MajorAxisIsyAxis, F''_{12}, F''_{22}) → F''_{2}
57. Intersect(t_{1y}, t_{2x}) → N
58. FirstAxis(h) → e_{x}
59. SecondAxis(h) → e_{y}
60. Line(T_{2x}, T_{1x}) → l_{t2xt1x}
61. Intersect(l_{t2xt1x}, xAxis) → R_{x}
62. OrthogonalLine(R_{x}, xAxis) → l_{r11}
63. If(h'IsHyperbola, Hyperbola[F''_1, F''_{2}, V''_{2}], Ellipse[F''_1, F''_{2}, V''_{2}]) → h''
64. Intersect(h'', xAxis) → R_1, R_{11}
65. Line(Point[{0, (-x(R_{11}))}], xAxis) → l_{r22}
66. Excentricity(h) → c
67. Eccentricity(h) → e
68. Polar(M, h) → t
69. Mirror(t, e_{x}) → t'
70. Tangent(M, h) → q,
71. Segment(F_{1}, A) → s_{a1}
72. Segment(F_{2}, P_{C1}) → s_{b1}
73. Segment(F_{1}, P_{C1}) → s_{e12}
74. Segment(A, F_{2}) → s_{d21}
75. Segment(F_{1}, B) → s_{e22}
76. Segment(F_{2}, P_{B1}) → s_{d12}
77. Segment(A, P_{B1}) → s_{a2}
78. Segment(P_{C1}, B) → s_{b2}
79. OrthogonalLine(F_{2}, yAxis) → l_{f2xAxis}
80. Intersect(c_{1}, l_{f2xAxis}) → G, H
81. Line(H, F_{1}) → l_{f1t1y}
82. Line(F_{1}, G) → l_{f1t2y}
83. Line(F_{2}, D) → l_{f2t2y}
84. Line(F_{2}, F) → l_{f2t1y}
85. PointIn(h) → Pointh
86. Asymptote(h) → l_{a2}, l_{a1}
87. Vertex(h) → V_{1}, V_{2}, V_{3}, V_{4}
88. SecondAxisLength(h) → b
89. SecondAxisLength(h') → b'
90. Excentricity(h') → c'
91. Eccentricity(h') → e'
92. Intersect(o, t'_{1y}) → E, I
93. Intersect(t_{1x}, t_{1y}) → O
94. Intersect(l_{r22}, l_{r11}) → R_{22}
95. FirstAxisLength(h'') → a''
96. SecondAxisLength(h'') → b''
97. Excentricity(h'') → c''
98. Intersect(t_{1y}, l_{f1t1y}) → T_{1y}
99. Intersect(t_{2y}, l_{f2t2y}) → T_{2y}
100. Segment(J, V'_{2}) → s_{f12}
101. Segment(K, V'_{2}) → s_{f11}
102. Segment(I, V'_{1}) → s_{f21}
103. Segment(E, V'_{1}) → s_{f22}
104. Intersect(t_{2x}, t_{2y}) → L
105. Segment(N, F'_{11}) → s_{g11}
106. Segment(O, F'_{11}) → s_{g12}
107. Segment(L, F'_{21}) → s_{g21}
108. Segment(F'_{21}, C) → s_{g22}
109. Segment(F''_{11}, E) → s_{h11}
110. Segment(F''_{11}, J) → s_{h12}
111. Segment(R_{x}, T_{1x}) → s_{j1}
112. Segment(R_{x}, T_{2x}) → s_{j2}
113. Segment(R_{x}, R_{22}) → s_{r2}
114. CircleArc(Point[{0, 0}], Point[{0, (-x(R_1))}], Point[{0, x(R_1)}]) → c_{aux1}
115. Segment(R_{22}, Point[{0, y(R_{22})}]) → s_{r22}
116. Line(Point[{0, x(R_{11})}], xAxis) → l_{r21}
117. Intersect(l_{r21}, l_{r11}) → R_{21}
118. Segment(R_{21}, Point[{0, y(R_{21})}]) → s_{r21}
119. Segment(R_{x}, R_{21}) → s_{r1}
120. Point(h') → z_{1}
121. Directrix(h) → d_{2}, d_{1}
122. Directrix(h') → d'_{2}, d'_{1}
123. Point({imaginary(z_{1}), real(z'_{11})}) → z''_{11}
124. Point({imaginary(z_{1}), real(z'_{12})}) → z''_{12}
125. If(Defined[T_{1x}] ∧ Defined[T_{1y}], true, false) → h'MajorAxisIsxAxis
126. FirstAxis(h') → e'_{x}
127. Circle(F'_{11}, (2 * a')) → c'_{1}
128. Circle(F'_{21}, (2 * a')) → c'_{2}
129. Intersect(c'_{2}, t_{1y}) → P, Q
130. LineBisector(Q, F'_{11}) → t'_{2x}
131. LineBisector(F'_{11}, P) → t'_{1x}
132. Intersect(t'_{1x}, t'_{2y}) → R
133. Circle(M', R) → o'
134. Radius(o') → r'
135. If(h'IsEllipse, Intersect[t_{1x}, yAxis]) → V''_{3}
136. Segment(O, If[h'IsHyperbola, V''_{1}, V''_{3}]) → s_{i11}
137. Segment(If[h'IsHyperbola, V''_{1}, V''_{3}], C) → s_{i12}
138. Segment(If[h'IsHyperbola, V''_{2}, V''_{4}], L) → s_{i22}
139. Segment(N, If[h'IsHyperbola, V''_{2}, V''_{4}]) → s_{i21}
140. Segment(F''_{12}, I) → s_{h21}
141. Segment(F''_{12}, K) → s_{h22}
142. Eccentricity(h'') → e''
143. FirstAxis(h'') → e''_{x}
144. SecondAxis(h'') → e''_{y}
145. Segment(T_{2x}, V'_{2}) → s_{f1d}
146. Segment(T_{1x}, V'_{1}) → s_{f2d}