MathPlotAI Logo MathPlotAI

Hyperbola Graphing

Hyperbola Graphing
Loading the math board and drawing, please wait…
2018-12-09 11:16
FunctionCoordinate GeometryGeometric ConstructionGraphing
This example demonstrates the graphing of hyperbolas and their properties, involving core math concepts like hyperbola definition, foci, asymptotes, and coordinate geometry. Construction highlights include GeoGebra commands such as Hyperbola, Circle, Line, Intersect, Segment, Midpoint, Polygon, Point, and SurdText. Suitable for high school mathematics education and learning to understand the geometric and algebraic characteristics of hyperbolas.

GeoGebra Commands & Parameters

  1. Hyperbola(F2, F1, A1) → d
  2. Hyperbola(F3, F4, A4) → e
  3. If(h ≟ 0, "x²", "(" + f + ")²") → tx
  4. If(k ≟ 0, "y²", "(" + g + ")²") → ty
  5. Circle(O, F3) → p
  6. Line(A3, xAxis) → l
  7. Line(A4, xAxis) → m
  8. Intersect(p, l) → A, B
  9. Intersect(p, m) → C, D
  10. Segment(A, B) → q
  11. Segment(D, B) → r
  12. Segment(A, C) → s
  13. Segment(D, C) → t
  14. Line(C, B) → f_1
  15. Line(A, D) → g_1
  16. Midpoint(A, C) → E
  17. Midpoint(B, D) → F
  18. Segment(A3, A4) → h_1
  19. Segment(E, F) → i_1
  20. Circle(O, F1) → c_1
  21. Line(A1, yAxis) → j_1
  22. Line(A2, j_1) → k_1
  23. Intersect(c_1, k_1) → G, H
  24. Intersect(c_1, j_1) → I, J
  25. Line(G, J) → l_1
  26. Line(H, I) → m_1
  27. Polygon(H, G, I, J) → q1, h_2, g_2, i_2, j_2
  28. Midpoint(H, J) → K
  29. Midpoint(G, I) → L
  30. Segment(K, L) → n_1
  31. Segment(A2, A1) → p_1
  32. Point(d) → M
  33. Segment(F2, M) → q_1
  34. Segment(M, F1) → r_1
  35. Point(e) → N
  36. Segment(F3, N) → s_1
  37. Segment(N, F4) → t_1
  38. If(Mod[b, 1] ≟ 0, "" + b, text14) → bo
  39. SurdText(a / b) → text16
  40. SurdText(b / a) → text17

AI Drawing Prompt Reference

Draw a hyperbola with foci at points F1 and F3, and vertices at points A1 and A4, using the Hyperbola command to create hyperbolas d and e. Draw lines from the foci to the vertices, construct the asymptotes, mark the foci and vertices, and display the eccentricity and equations of the asymptotes.
The prompt above was compiled from the original drawing commands and is for reference only.