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Drawing a Hyperbola

Drawing a Hyperbola
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2019-04-09 01:14
FunctionCoordinate GeometryGeometric Construction
In collections Exploring Conic Sections
This applet demonstrates how a hyperbola is constructed. It involves key concepts of hyperbolas and uses GeoGebra commands such as Circle, Line, Intersect, Rotate, Tangent, and Hyperbola. Suitable for high school mathematics, particularly for learning coordinate geometry and function graphs.

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 to demonstrate its construction. Start by creating two circles, then draw a line intersecting one circle to get a point. Rotate this point around the circle's center, connect the rotated point to the center, and draw the tangent at this point. Find the other intersection of the tangent with the circle, and use this point to draw a new circle. Finally, construct the hyperbola using these points and lines, clearly showing the formation process, and label key points and auxiliary lines.
The prompt above was compiled from the original drawing commands and is for reference only.