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Parabola as a Locus: Animated Definition

Parabola as a Locus: Animated Definition
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2016-05-02 10:46
Coordinate GeometryGeometric ConstructionSlider AnimationLocus
In collections Conic Sections Conic Sections- Maths Made Easy CCSS High School: Geometric Properties of Parabola
① This applet provides an animated illustration of the definition of a parabola as the locus of points equidistant from a fixed point (focus) and a fixed line (directrix). ② The core mathematical concept is the geometric definition of a conic section, specifically the equal-distance property that characterizes a parabola. ③ The construction uses GeoGebra commands such as Line, Parabola, Point, OrthogonalLine, Intersect, Dilate, Segment, Angle, and Rotate, along with a button to control the animation, showing how a moving point maintains equal distances to the focus and directrix. ④ It is suitable for middle school or high school geometry and algebra classes, helping students visualize the fundamental definition of a parabola and supporting interactive exploration of its properties.

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

Create an animation illustrating the definition of a parabola as the locus of points equidistant from a fixed focus and a fixed directrix. Show a point moving along the parabola, always maintaining equal distances to the focus and directrix. Use a slider to control the animation and display the relationship between the moving point, the focus, and the directrix to help visualize the geometric definition of a parabola.
The prompt above was compiled from the original drawing commands and is for reference only.