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Advanced Hyperbola Demonstration

Advanced Hyperbola Demonstration
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2014-11-25 22:06
Coordinate GeometryGeometric ConstructionLocus
This example demonstrates that the difference of distances from any point on a hyperbola to its foci is constant. It involves core math concepts like hyperbola definition, foci, distance formulas, and coordinate geometry. Constructed using GeoGebra commands: Point, Hyperbola, Segment, Distance. Suitable for high school students and math enthusiasts learning hyperbola properties and geometric constructions.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Hyperbola(A, B, C) → c
  4. Point(c) → D
  5. Segment(A, D) → a
  6. Segment(D, B) → b
  7. Distance(A, D) → distanceAD
  8. Distance(D, B) → distanceDB
  9. Point(c) → E
  10. Segment(A, E) → e
  11. Segment(E, B) → f
  12. Distance(E, B) → distanceEB
  13. Distance(E, A) → distanceEA

AI Drawing Prompt Reference

Draw a hyperbola and label its two foci. From any point on the hyperbola, draw the distances to both foci, demonstrating that the difference of these distances is constant. Start by plotting two points on the x-axis as the foci, then construct the hyperbola using these points and a constant. Next, select a point on the hyperbola, draw line segments from this point to each focus, calculate the lengths of these segments, and show that their difference remains constant.
The prompt above was compiled from the original drawing commands and is for reference only.