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Locus Definition of a Parabola

Locus Definition of a Parabola
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2016-07-01 09:44
VectorInequalityLocus
In collections Algebra 1
This applet provides an animated illustration of the locus definition of a parabola, demonstrating that it is the set of points equidistant from a fixed point (focus) and a fixed line (directrix). Key math concepts include parabola, vectors, addition, geometric distribution, inequalities, and cubes. It is constructed using GeoGebra commands like Line, Parabola, Point, OrthogonalLine, Intersect, Dilate, Segment, Angle, Rotate, targeting high school and above students for understanding the geometric definition and properties of parabolas.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Parabola(C, a) → c
  3. Point(c) → D
  4. OrthogonalLine(D, a) → b
  5. Intersect(a, b) → E
  6. Dilate(C, If[0 < d ≤ 1, 1 - d, 0], D) → C'
  7. Segment(C, C') → e
  8. Dilate(D, If[1 < d ≤ 2, 2 - d, 0], E) → D'
  9. Segment(D, D') → f
  10. Angle(A, E, D) → α
  11. Angle(E, D, C) → β
  12. Rotate(C, If[2 < d ≤ 3, ((-(d - 2)) * β), (-β)], D) → C'_1
  13. Rotate(C', If[2 < d ≤ 3, ((-(d - 2)) * β), (-β)], D) → C''
  14. Segment(C'_1, C'') → e'

AI Drawing Prompt Reference

Draw a parabola with a fixed focus point and a horizontal directrix line. Place a moving point on the parabola, and drop a perpendicular from it to the directrix, marking the foot. Connect the focus to the moving point, and the moving point to the foot, forming two segments. Then create an auxiliary point such that its distance from the focus varies with an animation parameter, and connect the focus to this auxiliary point. Finally, rotate both the focus and the auxiliary point around the moving point by an angle controlled by the same parameter, producing a dynamic segment that illustrates the equal-distance property of the parabola.
The prompt above was compiled from the original drawing commands and is for reference only.