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Ellipse: Focal Property Demo

Ellipse: Focal Property Demo
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2023-03-17 00:21
VectorTrigonometryCoordinate GeometryGeometric Construction
In collections geometriadinamica.es
This example demonstrates the focal property of an ellipse: the sum of distances from any point on the ellipse to the two foci is constant. Key math concepts include ellipse definition, foci, distance formulas, and coordinate geometry. Construction involves commands like Point, Intersect, Ray, Circle, Rotate, Segment, Vector, Tangent to create the ellipse, foci, and dynamic elements. Suitable for high school coordinate geometry instruction to visualize ellipse geometric properties.

GeoGebra Commands & Parameters

  1. Point(xAxis) → AA
  2. Point(yAxis) → BB
  3. Intersect(xAxis, yAxis) → O
  4. Ray(O, BB) → semi_b
  5. Point(semi_b) → B
  6. Circle(O, B) → q
  7. Ray(O, AA) → semi_a
  8. Intersect(q, semi_a, 1) → I
  9. Ray(I, AA) → m
  10. Point(m) → A
  11. Ray(F, A) → e
  12. Rotate(F, α, F) → F'_1
  13. Rotate(A, α, F) → A'_1
  14. Ray(F'_1, A'_1) → f
  15. Intersect(d, f, 1) → C
  16. Segment(F, G) → h
  17. Vector(C, H) → i
  18. Tangent(C, d) → j,
  19. Circle(C, k) → p
  20. Intersect(p, j) → D, E
  21. Segment(((1 + sgn(rr - 1)) * E) + (sgn(rr - 1) * (100, 100)), ((1 + sgn(rr - 1)) * D) + (sgn(rr - 1) * (100, 100))) → l

AI Drawing Prompt Reference

Draw an ellipse. The ellipse has two foci, and the sum of distances from any point on the ellipse to the two foci is constant. Include the ellipse, the two foci, and an auxiliary line. The construction order should start from the center point, then draw the foci, then the ellipse, and finally add the auxiliary line to show the relationship between the foci and the ellipse.
The prompt above was compiled from the original drawing commands and is for reference only.