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Parabola Defined by Focus and Directrix

Parabola Defined by Focus and Directrix
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2015-11-13 23:36
FunctionCoordinate GeometryGeometric Construction
This example demonstrates constructing a parabola using a focus and directrix. Key mathematical concepts include the definition of a parabola, geometric construction, and coordinate geometry. Commands used include Line, Parabola, OrthogonalLine, Intersect, Point, Segment, etc. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(A, B) → directrix
  2. Parabola(focus, directrix) → parabola
  3. OrthogonalLine(focus, directrix) → b
  4. Intersect(directrix, b) → D
  5. Intersect(parabola, b, 1) → vertex
  6. Point(parabola) → G
  7. Point(parabola) → H
  8. Point(parabola) → I
  9. Point(parabola) → J
  10. Point(parabola) → K
  11. OrthogonalLine(K, directrix) → d
  12. OrthogonalLine(J, directrix) → e
  13. OrthogonalLine(G, directrix) → g
  14. OrthogonalLine(H, directrix) → h
  15. OrthogonalLine(I, directrix) → i
  16. Intersect(directrix, d) → L
  17. Intersect(directrix, e) → M
  18. Intersect(directrix, g) → O
  19. Intersect(directrix, h) → P
  20. Intersect(directrix, i) → Q
  21. Segment(focus, J) → j
  22. Segment(J, M) → k
  23. Segment(focus, K) → l
  24. Segment(K, L) → m
  25. Segment(focus, G) → q
  26. Segment(G, O) → r
  27. Segment(H, focus) → s
  28. Segment(H, P) → t
  29. Segment(focus, I) → a_1
  30. Segment(I, Q) → b_1