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Ellipse/Hyperbola Reflection

Ellipse/Hyperbola Reflection
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2016-05-20 10:23
Coordinate GeometryTransformationGeometric ConstructionLocus
This example demonstrates the reflection properties and loci of ellipses and hyperbolas. It involves core mathematical concepts such as ellipses, hyperbolas, reflections, circles, correlation, percentages, kites, and addition. The construction uses GeoGebra commands like Ellipse, Circle, Point, Mirror, Locus, Midpoint, Hyperbola, and objects like a, A, B, k, r, C, c, m, D, d, E, E', loc1, F, G, e, H, H'. Suitable for high school and above students to understand the geometric properties and transformations of conic sections.

GeoGebra Commands & Parameters

  1. Ellipse(B, A, C) → c
  2. Circle(D, r) → d
  3. Point(c) → E
  4. Mirror(E, d) → E'
  5. Locus(E', E) → loc1
  6. Midpoint(A, B) → F
  7. Hyperbola(B, A, G) → e
  8. Point(e) → H
  9. Mirror(H, d) → H'
  10. Locus(H', H) → loc2

AI Drawing Prompt Reference

Draw an ellipse and a hyperbola sharing two common foci. Construct a circle with the segment between the foci as its diameter, serving as a mirror. Pick a point on the ellipse, reflect it across the circle to get its image, and trace the locus of that image as the point moves along the ellipse. Similarly, pick a point on the hyperbola, reflect it across the same circle, and trace the locus of its image. The final figure includes the ellipse, hyperbola, mirror circle, two traced loci, and the relevant foci and auxiliary points, illustrating the transformation of conic sections under circular reflection.
The prompt above was compiled from the original drawing commands and is for reference only.