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Parabola: Formation and Effect

Parabola: Formation and Effect
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2018-06-24 21:52
Locus
In collections GeoGebra 3D & AR: PreCalc & Calculus Resources
This example demonstrates the formation and geometric properties of a parabola, a specific conic section. Using GeoGebra commands such as IntersectPath, Line, Distance, etc., the focus and vertex of the parabola are constructed. Suitable for high school mathematics education, it helps students understand the geometric construction and properties of parabolas.

GeoGebra Commands & Parameters

  1. IntersectPath(c, a) → d
  2. Line((0, 0, 0), (1, 0, 1)) → f
  3. Line(A, f) → g
  4. Distance(A, (0, 0, 0)) → e
  5. Sphere(A, (0.4 * e)) → h
  6. IntersectPath(y = 0, h) → k
  7. Intersect(g, k) → B, C
  8. Intersect(xAxis, k) → D, E
  9. Rotate(D, If[0 < i ≤ 1, ((-i) * π / 4), ((-π)) / 4], A, Line[(4, 0, 0), (4, 1, 0)]) → D'
  10. CircleSector(A, D, D') → p
  11. Dilate(A, If[1.5 < i ≤ 2.5, 2.5 - i, 0], (0, 0, 0)) → A'
  12. Vector(A, A') → u
  13. Translate(p, u) → p'
  14. Line(A, (x(A), y(A) + 1, 0)) → l
  15. Rotate(j, ((-m) * π / 180), l) → j'
  16. IntersectPath(j', a) → q
  17. Line((100, 0, 0), A) → n
  18. Focus(q) → F, G
  19. Point(q) → H
  20. Vertex(q) → I, , ,
  21. Sphere(I, F) → c_1
  22. Intersect(g, c_1) → J, K
  23. Sphere(K, I) → e_1
  24. Intersect(g, e_1) → L, M
  25. LineBisector(L, K, Plane[H, F, K]) → f_1
  26. Intersect(g, f_1) → N
  27. Dilate(F, If[4 < i ≤ 5, 5 - i, 0], H) → F'
  28. Segment(F, F') → g_1
  29. Line(H, g) → h_1
  30. Intersect(f_1, h_1) → O
  31. Intersect(f_1, g) → P
  32. Angle(F, H, O) → β
  33. Rotate(F, If[5 < i ≤ 6, ((-(i - 5)) * β), (-β)], H, Plane[F, H, P]) → F'_1
  34. Rotate(F', If[5 < i ≤ 6, ((-(i - 5)) * β), (-β)], H, Plane[F, H, P]) → F''
  35. Segment(F'_1, F'') → i_1
  36. Vector(P, K) → u_1
  37. Translate(f_1, u_1) → j_1
  38. Intersect(j_1, h_1) → Q
  39. Angle(H, Q, K) → α

AI Drawing Prompt Reference

Draw a parabola with vertex A and focus F. First, construct the parabola using point A and line f, then use point A and point F to construct a circle intersecting line f at points B and C. Next, construct a conic section using point A and point D, intersecting line f at points J and K, then construct the directrix f1 using points J and K, intersecting line f at point N. Finally, construct a circle using point F and point H, intersecting line f at points L and M, then construct the axis f1 using points L and K, intersecting line f at points O and P.
The prompt above was compiled from the original drawing commands and is for reference only.