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Vertical Parabolas: Focus, Directrix, and Latus

Vertical Parabolas: Focus, Directrix, and Latus
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2015-05-31 05:23
FunctionCoordinate GeometryGeometric ConstructionSlider Animation
This example demonstrates the geometric properties of vertical parabolas, including the focus, directrix, and latus rectum, with dynamic relationships. Key math concepts involved: parabola definition, focus-directrix distance, focal chord length, coordinate geometry. Construction highlights: utilizes GeoGebra commands like Point, OrthogonalLine, Intersect, Segment, Angle, Distance, Line, and Midpoint to build the parabola and its associated elements. Suitable for high school coordinate geometry instruction or exploration by math enthusiasts.

GeoGebra Commands & Parameters

  1. Point(Directrix) → RandomPointonDirectrix
  2. OrthogonalLine(RandomPointonDirectrix, Directrix) → b
  3. Intersect(c, b) → B, D
  4. Segment(Focus, B) → d
  5. Point(Directrix) → C
  6. Angle(B, RandomPointonDirectrix, C) → α
  7. Segment(RandomPointonDirectrix, B) → e
  8. Distance(Focus, B) → distanceFocusB
  9. Distance(RandomPointonDirectrix, B) → distanceAB
  10. Segment(Focus, D) → f
  11. Segment(RandomPointonDirectrix, D) → g
  12. Angle(C, RandomPointonDirectrix, D) → β
  13. Distance(Focus, D) → distanceFocusD
  14. Distance(D, RandomPointonDirectrix) → distanceDRandomPointonDirectrix
  15. Segment(Focus, Vertex) → i
  16. OrthogonalLine(Vertex, Directrix) → j
  17. Intersect(j, Directrix) → A
  18. Segment(A, Vertex) → l
  19. Distance(Focus, Vertex) → distanceFocusVertex
  20. Distance(Vertex, A) → distanceVertexA
  21. Line(Focus, Directrix) → m
  22. Intersect(c, m) → E, F
  23. Segment(E, F) → n
  24. Segment(E, F) → q
  25. Distance(E, F) → distanceEF
  26. Midpoint(E, F) →
  27. Distance(Vertex, Focus) → distanceVertexFocus
  28. Midpoint(Vertex, Focus) →
  29. Distance(Vertex, A) → a
  30. Midpoint(Vertex, A) →