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Focus-Directrix Property Demo

Focus-Directrix Property Demo
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2018-04-06 09:44
VectorFunctionCoordinate GeometryGeometric Construction
In collections Conic sections
This example demonstrates the focus-directrix property of a parabola, showing that the distance from any point on the parabola to its focus equals the distance to its directrix. It involves core concepts like parabola definition, focus, directrix, and distance formulas. Constructed using commands such as Point, Line, Vector, Intersect, and Segment to visualize and verify the property. Suitable for high school coordinate geometry instruction or student exploration of parabola properties.

GeoGebra Commands & Parameters

  1. Point(zAxis) → A
  2. Line(A, B) → f
  3. Vector(A, A + (10 * (B - A))) → u
  4. InfiniteCone(A, u, (π * α / 180)) → a
  5. IntersectPath(d, a) → c
  6. Focus(c) → D, E
  7. OrthogonalLine(D, d) → h
  8. Intersect(h, f) → G
  9. Point(c) → H
  10. Line(A, H) → m
  11. OrthogonalLine(G, m, space) → f_1
  12. OrthogonalLine(E, d) → i
  13. Intersect(i, f) → F
  14. OrthogonalLine(F, m, space) → t
  15. PointIn(a) → C
  16. Line(A, C) → g
  17. Angle(g, f) → β
  18. Sphere(G, D) → b
  19. Sphere(F, E) → e
  20. OrthogonalPlane(F, u) → l
  21. Segment(H, E) → n
  22. Segment(H, D) → q
  23. OrthogonalPlane(G, u) → o
  24. Intersect(t, m) → I
  25. Segment(H, I) → j
  26. Intersect(f_1, m) → J
  27. Segment(J, H) → s
  28. Line(A, A + u) → g_1
  29. Circle(g_1, I) → c_1
  30. Circle(g_1, J) → d_1
  31. Plane(c_1) → p
  32. Plane(d_1) → r
  33. IntersectPath(r, d) → h_1
  34. IntersectPath(p, d) → i_1
  35. OrthogonalLine(H, h_1, xOyPlane) → j_1
  36. Intersect(i_1, j_1) → L
  37. Intersect(h_1, j_1) → K
  38. Segment(K, H) → k_1
  39. Segment(H, L) → l_1

AI Drawing Prompt Reference

Draw a parabola to demonstrate the focus-directrix property, showing that the distance from any point on the parabola to its focus equals the distance to its directrix. Start by plotting the parabola, marking its focus and directrix. Draw perpendicular lines from the focus to the directrix and from the intersection point to the parabola. Then, create vectors from the focus and directrix to form a cone, marking its intersection with the parabola. Finally, draw line segments from the intersection points to the focus and directrix to verify equal lengths.
The prompt above was compiled from the original drawing commands and is for reference only.