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Conic Sections Generation: Rotating Plane Cutting Cone

Conic Sections Generation: Rotating Plane Cutting Cone
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2015-08-14 23:55
Coordinate GeometrySolid GeometryGeometric ConstructionSlider Animation
This example demonstrates the generation of conic sections by rotating a plane to intersect a cone. It covers core concepts like ellipse, hyperbola, and parabola. Construction uses GeoGebra commands such as Cone, Plane, Rotate, and Intersect to build the 3D model and dynamic intersection curves. Suitable for high school or college math education to visualize conic section origins.

GeoGebra Commands & Parameters

  1. Point(zAxis) → A
  2. Intersect(xAxis, yAxis) → B
  3. Cone(A, B, 2) → a, c, b
  4. Point(zAxis) → C
  5. Cone(C, B, 2) → d, e, f
  6. Point(zAxis) → D
  7. Plane(H, G, F) → g
  8. Segment(F, G) → i
  9. Rotate(g, (n * π), i) → g'
  10. IntersectPath(g', d) → h
  11. Corner(h) → I, J
  12. IntersectPath(g', a) → k
  13. Corner(k) → K, L
  14. PointIn(g') → M
  15. PointIn(g') → N
  16. PointIn(g') → O
  17. PointIn(g') → P
  18. Polygon(M, P, O, N) → poly1, m, p, o, n_1

AI Drawing Prompt Reference

Draw a parabola generated by cutting a cone with a plane. Show the cone, the plane, and the resulting curve. Keep the drawing simple and clear to illustrate the geometric relationship.
The prompt above was compiled from the original drawing commands and is for reference only.