Drawing a Hyperbola by Jennifer Silverman

Drawing a Hyperbola by Jennifer Silverman
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2013-05-20 04:57
This applet demonstrates how a hyperbola is constructed. Using GeoGebra commands such as Circle, Intersect, Rotate, and Hyperbola, students can visually see the construction process. Suitable for high school mathematics, particularly in coordinate geometry and function graphing.

GeoGebra Commands & Parameters

  1. Circle(A_2, w) → c
  2. Circle(A_2, h) → d
  3. Line(A_2, xAxis) → e
  4. Intersect(c, e, 2) → B_2
  5. Rotate(B_2, α, A_2) → B
  6. Tangent(B, c) → f,
  7. Line(B, A_2) → g
  8. Intersect(c, g, 2) → A
  9. Tangent(A, c) → h_2,
  10. Circle(A, h) → k
  11. Circle(A, Radius[c]) → p
  12. Circle(B, Radius[d]) → q
  13. Circle(A, w) → r
  14. Circle(B, h) → s
  15. Intersect(r, s, 1) → I
  16. Hyperbola(A, B, I) → t
  17. Point(t) → D
  18. Intersect(t, e, 2) → E
  19. OrthogonalLine(E, e) → i
  20. Intersect(t, e, 1) → F
  21. OrthogonalLine(F, e) → j
  22. Distance(E, F) → distanceEF
  23. Circle(A_2, Segment[A_2, B]) → c_1
  24. Intersect(c_1, j, 1) → G
  25. OrthogonalLine(G, j) → l
  26. Intersect(c_1, j, 2) → H
  27. OrthogonalLine(H, j) → m
  28. Intersect(c_1, i, 1) → J
  29. Intersect(c_1, i, 2) → K
  30. Polygon(H, G, J, K) → poly1, h_1, g_1, j_1, k_1
  31. Line(J, H) → n
  32. Line(G, K) → a_1
  33. Segment(D, A) → s_1
  34. Segment(D, B) → s_2
  35. Segment(A_2, F) → a
  36. Distance(E, F) → a_2
  37. OrthogonalLine(A_2, a) → b_2
  38. Intersect(g_1, b_2) → L
  39. Segment(A_2, L) → b
  40. Circle(A_1, g_2) → h_3
  41. Circle(B_1, e_1) → k_2
  42. Intersect(h_3, k_2, 1) → C_1
  43. Ellipse(A_1, B_1, C_1) → p_1
  44. Line(A_1, B_1) → i_1
  45. Point(p_1) → B'_1
  46. Segment(A_1, B'_1) → j_2
  47. Segment(B_1, B'_1) → l_1
  48. Segment(A_1, B_1) → a_3
  49. Midpoint(a_3) → G_1
  50. OrthogonalLine(G_1, a_3) → b_3
  51. Intersect(p_1, b_3) → F_1, E_1
  52. Line(A_1, B_1) → c_2
  53. Intersect(p_1, c_2) → C_2, D_1
  54. Distance(G_1, D_1) → distanceGD_1
  55. Distance(G_1, E_1) → distanceGE_1
  56. Segment(G_1, E_1) → b_4
  57. Segment(G_1, D_1) → a_4

AI Drawing Prompt Reference

Draw a hyperbola with foci at points A and B, which are on opposite sides of line e. Start by drawing two circles c and d, then use rotation and intersection to find the focus I of the hyperbola. Construct the hyperbola t using points A, B, and I, and locate the vertices D and E on line e. Use the perpendicular lines from E and F to find the asymptotes i and j, and finally determine the shape of the hyperbola.
The prompt above was compiled from the original drawing commands and is for reference only.