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Cones and Conic Sections

Cones and Conic Sections
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2019-04-21 19:16
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the formation and properties of cones and their conic sections (circle, ellipse, hyperbola, parabola). It involves core concepts like cones, conic sections, foci, directrices, and analytical geometry. Construction highlights include using GeoGebra commands such as Cone, Line, IntersectPath, Plane, and Rotate. Suitable for high school mathematics students and teachers to understand the conic section theorem and the geometric definitions of quadratic curves.

GeoGebra Commands & Parameters

  1. Cone((0, 0, 3), (0, 0, 9), 8) → a, a_2, a_3
  2. Cone((0, 0, 9 - (5 * 3)), (0, 0, 9), (5 * 4)) → b, c, d
  3. Line((6, 0, 6), (6, 1, 6)) → f
  4. IntersectPath(Plane[(6, 0, 0), f], d) → e
  5. IntersectPath(Plane[(8, 0, 0), f], d) → g
  6. IntersectPath(Plane[(10, 0, 0), f], d) → h
  7. IntersectPath(Plane[(4, 0, 0), f], d) → k
  8. IntersectPath(Plane[(2, 0, 0), f], d) → p
  9. IntersectPath(Plane[(0, 0, 0), f], d) → q
  10. IntersectPath(Plane[(-2, 0, 0), f], d) → r
  11. IntersectPath(Plane[(-6, 0, 0), f], d) → s
  12. IntersectPath(Plane[(0, 0, 6), f], d) → t
  13. IntersectPath(Plane[(0, 0, 8), f], d) → c_1
  14. IntersectPath(Plane[(0, 0, 7), f], d) → d_1
  15. IntersectPath(Plane[(0, 0, 5), f], d) → e_1
  16. IntersectPath(Plane[(0, 0, 4), f], d) → f_1
  17. Plane((0, 0, 8), f) → i
  18. Rotate(i, n, f) → i'
  19. IntersectPath(i', b) → g_1