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Conic Sections by Nadezhda Konstantinova

Conic Sections by Nadezhda Konstantinova
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2014-10-11 02:41
TrigonometryCoordinate Geometry
This example demonstrates the generation process of conic sections, including ellipses, parabolas, and hyperbolas. It involves basic concepts of conic sections and uses GeoGebra commands such as Point, Circle, Intersect, etc., to construct these curves. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Circle(zAxis, A) → c
  3. Intersect(xAxis, c, 1) → E
  4. Intersect(xAxis, c) → F, G
  5. OrthogonalLine(G, xOyPlane) → j
  6. Point(j) → J
  7. Circle(J, G, E) → k
  8. Point(zAxis) → B
  9. Circle(B, 2, zAxis) → d
  10. Cone(c, 2) → a_1, e, b
  11. Cone(d, -2) → f, g, h
  12. Point(zAxis) → D
  13. Line(D, yAxis) → i
  14. Intersect(j, d) → H,
  15. PointIn(h) → I
  16. Point(k) → K
  17. Point(g) → C
  18. Plane(K, C, B) → a
  19. Rotate(K, 360, (0, 0, 0), xOyPlane) → K'
  20. Rotate(K, α, C, xOyPlane) → K'_1
  21. Rotate(K, α, C, xOyPlane) → K'_2
  22. Line(C, yAxis) → m
  23. Point(m) → N
  24. Line(N, m) → n
  25. Rotate(K, α, m) → K'_3
  26. Plane(K'_3, i) → l
  27. IntersectPath(l, xOyPlane) → p
  28. IntersectPath(l, b) → q
  29. IntersectPath(l, b) → r
  30. Intersect(yAxis, zAxis) → L
  31. Segment(B, L) → s
  32. Intersect(s, l) → M
  33. OrthogonalLine(M, p, l) → t
  34. IntersectPath(l, f) → c_1
  35. Corner(c_1) → O, P
  36. Line(G, C) → b_1
  37. Intersect(b_1, t) → Q
  38. Angle(M, Q, C) → γ

AI Drawing Prompt Reference

Draw a cone with ellipses, parabolas, and hyperbolas. Start by drawing a circle on the coordinate axes, then construct these curves using intersections and tangents. Next, draw a cone and generate different curves and planes through rotations and intersections, and finally create the final shape through intersections and rotations.
The prompt above was compiled from the original drawing commands and is for reference only.