Parabola Locus Definition Animation

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2020-10-20 22:48

This GeoGebra applet provides an animated illustration of the geometric definition of a parabola: the locus of points in a plane that are equidistant from a fixed point (focus) and a fixed line (directrix). Key mathematical concepts include the focus, directrix, and the locus property of parabolas. Construction uses Line for the directrix, Point for the focus and moving point on the parabola, OrthogonalLine to draw the perpendicular to the directrix, Intersect to find intersection points, Parabola command to generate the curve, with Dilate and Rotate for animation effects, and Segment to display the focal radius. This example is ideal for secondary school mathematics courses on coordinate geometry and conic sections, helping students visually understand the locus definition and geometric properties of parabolas.

GeoGebra Commands & Parameters

Line(A, B) → a
Parabola(C, a) → c
Point(c) → D
OrthogonalLine(D, a) → b
Intersect(a, b) → E
Dilate(C, If[0 < d ≤ 1, 1 - d, 0], D) → C'
Segment(C, C') → e
Dilate(D, If[1 < d ≤ 2, 2 - d, 0], E) → D'
Segment(D, D') → f
Angle(A, E, D) → α
Angle(E, D, C) → β
Rotate(C, If[2 < d ≤ 3, ((-(d - 2)) * β), (-β)], D) → C'_1
Rotate(C', If[2 < d ≤ 3, ((-(d - 2)) * β), (-β)], D) → C''
Segment(C'_1, C'') → e'

AI Drawing Prompt Reference

Create an animation illustrating the geometric definition of a parabola: the locus of points equidistant from a fixed point (focus) and a fixed line (directrix). Draw the directrix, then set the focus and a moving point. Draw a perpendicular from the moving point to the directrix and find the intersection point. Generate the parabola using the focus and intersection point. Animate the moving point to show its locus, draw the segment from the focus to the moving point, and display angle changes and rotation effects.

The prompt above was compiled from the original drawing commands and is for reference only.