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Animated Conic Sections

Animated Conic Sections
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2018-11-26 02:58
Coordinate GeometryParametric EquationLocus
This example demonstrates the generation process of conic sections through animation. Key mathematical concepts include the definition of conic sections, parametric equations, and loci. Using GeoGebra commands such as Cone, Circle, and IntersectPath, the dynamic changes in conic sections can be observed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Cone((0, 0, h), O, r) → a, c, b
  2. Cone((0, 0, (-h)), O, r) → d, e, f
  3. Circle(A, 1, nor) → g
  4. Plane(g) → i
  5. IntersectPath(i, d) → k
  6. IntersectPath(i, a) → p
  7. OrthogonalLine(A, i) → j
  8. If(θ ≟ 0, "Circle", If[θ < 45°, "Ellipse", If[θ ≟ 45°, "Parabola", If[(θ > 45°) ∧ (θ < 90°), "Hyperbola", "Rectangular Hyperbola"]]]) → text1