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Inverse of an Ellipse

Inverse of an Ellipse
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2015-04-23 07:20
Coordinate GeometryGeometric ConstructionLocus
This example demonstrates the inversion of an ellipse with respect to a circle centered at one of its foci, involving core math concepts like ellipse, inversion, locus, and coordinate geometry. It uses GeoGebra commands such as Ellipse, Circle, Point, Mirror, Locus, Midpoint, and Segment. Suitable for high school students and teachers exploring geometric transformations and locus properties.

GeoGebra Commands & Parameters

  1. Ellipse(F_2, F_1, C) → c
  2. Circle(O_c, D) → d
  3. Point(c) → M
  4. Mirror(M, d) → M'
  5. Locus(M', M) → loc1
  6. Midpoint(F_2, F_1) → O_E
  7. Segment(O_c, M') → e
  8. Segment(M, O_c) → b

AI Drawing Prompt Reference

Draw an ellipse with one focus as the center, create a circle centered at that focus, reflect points on the ellipse across the circle, trace the path of the reflected points, label the foci of the ellipse and the center of the circle, and connect the reflected points to the center of the circle and the original points on the ellipse to demonstrate the inversion transformation and locus properties.
The prompt above was compiled from the original drawing commands and is for reference only.