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Parabola: Points Equidistant from Focus and Directrix

Parabola: Points Equidistant from Focus and Directrix
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2015-07-21 04:25
Geometric ConstructionSlider Animation
This example demonstrates the geometric construction of a parabola. The core mathematical concept is the definition of a parabola: the set of points equidistant from the focus and the directrix. Construction involves GeoGebra commands such as Point, Intersect, Ray, and Segment to create the focus, directrix, and points. Suitable for middle or high school mathematics learning to understand the basic properties and construction of a parabola.

GeoGebra Commands & Parameters

  1. Point(b) → Focus
  2. Intersect(a, c) → B
  3. Point(c) → C
  4. Intersect(a, d) → D
  5. Point(d) → E
  6. Intersect(a, e) → F
  7. Point(e) → G
  8. Point(f) → H
  9. Intersect(a, f) → I
  10. Intersect(a, g) → J
  11. Point(g) → K
  12. Intersect(a, h) → L
  13. Point(h) → M
  14. Ray(L, M) → i
  15. Ray(J, K) → j
  16. Ray(I, H) → k
  17. Ray(B, C) → l
  18. Ray(D, E) → m
  19. Ray(F, G) → n
  20. Intersect(a, b) → N
  21. Point(b) → O
  22. Ray(N, O) → p
  23. Segment(Focus, O) → q
  24. Segment(Focus, C) → s
  25. Segment(C, B) → t
  26. Segment(Focus, E) → a_1
  27. Segment(E, D) → b_1
  28. Segment(Focus, G) → c_1
  29. Segment(G, F) → d_1
  30. Segment(Focus, H) → e_1
  31. Segment(H, I) → f_1
  32. Segment(Focus, K) → g_1
  33. Segment(K, J) → h_1
  34. Segment(Focus, M) → i_1
  35. Segment(M, L) → j_1
  36. Segment(O, N) → r

AI Drawing Prompt Reference

Draw a parabola demonstrating its geometric definition: the set of points equidistant from a focus and a directrix. Start with a horizontal line as the directrix and place a point above it as the focus. Drop a perpendicular from the focus to the directrix to mark the vertex. Select several points on the directrix, connect each to the focus, and construct the perpendicular bisector of each segment. From each directrix point, draw a perpendicular line intersecting its bisector; these intersections lie on the parabola. Connect these points with a smooth curve to form the parabola. Finally, use dashed lines to show the segments from the focus to the directrix points and from those points to the intersections, illustrating equal distances.
The prompt above was compiled from the original drawing commands and is for reference only.