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Parabola Demonstration by Martin Cardenas

Parabola Demonstration by Martin Cardenas
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2017-04-12 01:47
Coordinate GeometryLimitOptimizationGeometric Construction
This example demonstrates the definition and geometric properties of a parabola, dynamically showing its shape through the positional relationship between the focus and directrix. Core mathematical concepts include the definition of a parabola, analytical geometry, distance formulas, and angle calculations. It utilizes commands and objects like Line, OrthogonalLine, Intersect, Segment, Midpoint, Angle, and Distance from GeoGebra for construction. Suitable for high school students and math enthusiasts learning about parabolas and geometric constructions.

GeoGebra Commands & Parameters

  1. Line(A, B) → DIRECTRIX
  2. OrthogonalLine(Focus, DIRECTRIX) → a
  3. Intersect(a, DIRECTRIX) → C
  4. Segment(Focus, C) → e
  5. Midpoint(Focus, C) → Vertex
  6. OrthogonalLine(Vertex, DIRECTRIX) → h
  7. Segment(Focus, F) → j
  8. OrthogonalLine(F, DIRECTRIX) → k
  9. Intersect(DIRECTRIX, k) → D
  10. Segment(F, D) → l
  11. Angle(F, D, A) → α
  12. Distance(Focus, Vertex) → distanceFocusm
  13. Intersect(DIRECTRIX, h) → E
  14. Distance(Vertex, E) → d
  15. Segment(Focus, Vertex) → n
  16. Segment(Vertex, E) → p
  17. Distance(j, l) → b