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Hyperbola as a Locus Definition

Hyperbola as a Locus Definition
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2012-01-27 19:57
Coordinate GeometryGeometric ConstructionLocus
This example visualizes the definition of a hyperbola as the locus of points where the absolute difference of distances to two fixed points is constant. Key math concepts include hyperbola definition, distance measurement, and coordinate geometry. Construction involves GeoGebra commands like Ray, Intersect, Segment, Distance, Polygon, and objects such as points F, F', and segments with calculated distances. Suitable for high school coordinate geometry students to grasp the geometric foundation of hyperbolas.

GeoGebra Commands & Parameters

  1. Ray(F', R) → e
  2. Intersect(d, e) → A, B
  3. Segment(B, F) → f
  4. Distance(F', B) → distanciaF'B
  5. Distance(B, F) → distanciaBF
  6. Polygon(F', F, B) → polígono1, b_1, f', f_1

AI Drawing Prompt Reference

Draw a hyperbola with foci F' and F, and point B on the hyperbola such that the absolute difference of distances from B to F' and F is constant. First, draw a ray through F', then find its intersection with line d to get points A and B. Next, draw segment BF and measure the distances distanciaF'B and distanciaBF. Finally, draw the circumpolygon of triangle F'BF.
The prompt above was compiled from the original drawing commands and is for reference only.