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Hyperbola Locus Construction

Hyperbola Locus Construction
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2015-07-03 09:51
Coordinate GeometryGeometric ConstructionLocus
In collections Conic Sections Conic Sections- Maths Made Easy
This example demonstrates the definition of a hyperbola as the set of all points in a plane such that the absolute difference of their distances to two fixed points (foci) is constant. It involves core concepts like hyperbola definition, coordinate geometry, and distance formula. Construction uses GeoGebra commands: Circle, Point, Segment, Midpoint, LineBisector, Intersect, Ray, Angle, Mirror. Suitable for high school students to learn and understand the geometric definition and construction of hyperbolas.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Segment(C, D) → a
  4. Midpoint(a) → M_1
  5. LineBisector(a) → p
  6. LineBisector(a) → d
  7. Intersect(p, d) → E
  8. Ray(A, C) → e
  9. Intersect(e, p) → H_1
  10. Segment(D, H_1) → f
  11. Segment(C, H_1) → g
  12. Segment(A, C) → h
  13. Angle(C, M_1, H_1) → α
  14. Mirror(A, A) → A'
  15. Mirror(C, A) → C'_2
  16. Segment(C, M_1) → k
  17. Segment(M_1, D) → l
  18. Angle(D, M_1, H_1) → β
  19. Segment(A, D) → b
  20. LineBisector(b) → i
  21. Mirror(H_1, i) → H_2

AI Drawing Prompt Reference

Draw a plane figure with two fixed points as foci and a constant length. Draw circles from each focus, mark the intersection as C. Connect C to the other focus D, find the midpoint and angle bisector. Draw a ray from focus A intersecting the bisector at H1, connect D to H1, and mark relevant segments and angles. Mirror C and H1 to get H2. Finally, display all points and lines to illustrate the hyperbola's definition of constant absolute difference.
The prompt above was compiled from the original drawing commands and is for reference only.