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Reflection of Ellipse Foci Across Its Tangents

Reflection of Ellipse Foci Across Its Tangents
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2015-06-10 06:24
CircleCoordinate GeometryTransformation
This example demonstrates the reflection of an ellipse's foci across its tangents. Key mathematical concepts include ellipses, reflections, and tangents. Using GeoGebra commands such as Ellipse, Tangent, and Mirror, the reflection effect can be visually observed. Suitable for high school mathematics education, particularly in coordinate geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Ellipse(A, B, C) → d
  2. Point(d, t) → D
  3. Tangent(D, d) → e,
  4. Mirror(A, e) → A'
  5. Mirror(B, e) → B'
  6. Ellipse(A', B', D) → c
  7. Circle(B, Distance[A, D] + Distance[B, D]) → f
  8. Segment(A, D) → a
  9. Segment(B, D) → b
  10. Segment(A', D) → g
  11. Segment(B', D) → h
  12. Circle(A, Distance[A, D] + Distance[B, D]) → k