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Conic Sections Demo by dorrod

Conic Sections Demo by dorrod
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2017-05-23 18:41
TrigonometrySolid GeometryGeometric Construction
This example demonstrates the various cross-sections formed by intersecting a cone with different planes. It involves core concepts like cones, cross-sections, geometric construction, and spatial geometry. The construction utilizes commands such as Intersect, Point, Line, Plane, Mirror, Ray, Angle, InfiniteCone, IntersectPath, AngularBisector, OrthogonalLine, Circle, Sphere, Segment, PointIn, OrthogonalPlane, and If. It is suitable for high school geometry education and geometric construction learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(zAxis) → B
  3. Line(C, yAxis) → a
  4. Plane(D, a) → b
  5. Mirror(C, D) → C'
  6. Ray(D, C') → c
  7. Angle(c, zAxis) → δ
  8. InfiniteCone(A, B, aa) → d
  9. IntersectPath(b, xz) → int
  10. IntersectPath(xz, d) → g
  11. Intersect(int, g) → V2, V1
  12. Line(A, V1) → c_1
  13. Line(A, V2) → c_2
  14. Line(A, B) → vert
  15. Point(c_2) → K
  16. IntersectPath(b, d) → r
  17. AngularBisector(c_1, int) → f, i
  18. Intersect(vert, f) → O2
  19. Intersect(vert, i) → O1
  20. OrthogonalLine(O2, c_1, xz) → j
  21. OrthogonalLine(O1, c_1, xz) → k
  22. Intersect(c_1, j) → G
  23. Intersect(c_1, k) → H
  24. Circle(O2, G, xz) → p
  25. Circle(O1, H, xz) → q
  26. Intersect(int, q) → F_1, J
  27. Intersect(int, p) → F_2, M
  28. Sphere(O1, F_1) → l
  29. Sphere(O2, F_2) → m
  30. Circle(zAxis, H) → tan2
  31. Circle(zAxis, G) → tan1
  32. Point(r) → Q
  33. Line(Q, A) → gen
  34. Intersect(gen, tan1) → E,
  35. Intersect(gen, tan2) → F,
  36. Segment(Q, F_2) → e
  37. Segment(Q, F) → n
  38. Segment(Q, F_1) → s
  39. Segment(Q, E) → t
  40. Circle(vert, Q) → d_1
  41. Plane(tan2) → o
  42. IntersectPath(o, b) → dir
  43. OrthogonalLine(Q, dir, b) → a_1
  44. Intersect(dir, a_1) → I
  45. OrthogonalLine(Q, a_1, b) → b_1
  46. Intersect(b_1, int) → L
  47. Intersect(dir, r) → N,
  48. Intersect(int, r) → O, P
  49. Intersect(dir, int) → R
  50. Segment(Q, I) → e_1
  51. Segment(L, R) → f_1
  52. Intersect(b_1, r) → S, T
  53. PointIn(b) → W
  54. OrthogonalPlane(R, dir) → u
  55. IntersectPath(u, d) → g_1
  56. Intersect(g_1, tan2) → U, V, ,
  57. Intersect(g_1, d_1) → Z, A_1, ,
  58. Segment(Z, U) → h_1
  59. If(bb < aa, text3, If[bb > aa, text1, text2]) → angle
  60. Angle(Q, I, R, b) → α
  61. Point(dir) → B_1
  62. Angle(F_1, R, B_1, b) → β