Ellipse – Geometric Definition Demo

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2016-02-15 08:19

In collections Conic Section Collection

① This example demonstrates the geometric definition of an ellipse: the locus of points whose sum of distances to two fixed foci is constant. ② Core concepts include ellipse, foci, major/minor axes, locus, distance definition, and the relationship between circles and segments. ③ Construction highlights: Points for foci and a moving point, Segments linking foci to the point, Circles centered at foci with equal radii, Intersect to find intersection points, Midpoint for auxiliary points, and Locus to trace the ellipse. ④ Suitable for high‑school geometry, analytic geometry, or conic sections lessons, and as a GeoGebra geometric construction and dynamic illustration resource.

GeoGebra Commands & Parameters

Point(a) → A
Point(a) → B
Segment(A, B) → b
Point(b) → C
Segment(A, C) → c
Segment(C, B) → d
Intersect(e, f) → D
Midpoint(b) → E
Intersect(e, g) → F
Intersect(e, h) → G
Segment(D, F) → i
Point(i) → H
Segment(H, F) → j
Circle(H, c) → k
Circle(I, d) → p
Intersect(k, p, 1) → J
Intersect(k, p, 2) → K
Segment(H, J) → l
Segment(H, K) → m
Segment(I, J) → n
Segment(I, K) → q
Locus(J, C) → loc1
Locus(K, C) → loc2

AI Drawing Prompt Reference

Draw an ellipse to demonstrate its geometric definition: the locus of points where the sum of distances to two fixed foci is constant. Start by marking two foci and drawing a line segment between them. Move a point along the segment, connecting it to each focus with a line. Create circles centered at the foci with radii equal to the lengths of these lines. The intersections of these circles give points on the ellipse. Finally, trace the path of these intersection points to form the ellipse.

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