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Ellipse Proof Construction

Ellipse Proof Construction
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2018-05-30 02:39
TrigonometryCoordinate Geometry
This example demonstrates the construction of an ellipse proof. Key mathematical concepts include the definition of an ellipse, tangents, orthogonal lines, and reflections. Using GeoGebra commands such as Ellipse, Tangent, OrthogonalLine, and Mirror, the geometric properties of the ellipse are visually illustrated. Suitable for high school mathematics education, particularly in coordinate geometry and calculus courses.

GeoGebra Commands & Parameters

  1. Ellipse(P, Q, A_1) → c
  2. Segment(A_1, P) → f
  3. Segment(A_1, Q) → g
  4. Tangent(A_1, c) → h,
  5. OrthogonalLine(Q, h) → i
  6. OrthogonalLine(P, h) → j
  7. Mirror(P, h) → P'
  8. Point(h) → B
  9. Intersect(h, f) → A
  10. Intersect(h, j) → X
  11. Intersect(h, i) → Y
  12. Segment(A, P') → k
  13. Angle(X, A, P) → α
  14. Angle(Q, A, Y) → β
  15. Point(h) → C
  16. Angle(C, X, P) → γ
  17. Point(h) → D
  18. Angle(Q, Y, D) → δ