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Geometric Parabola Construction

Geometric Parabola Construction
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2016-05-01 22:07
FunctionCoordinate GeometryTransformationGeometric Construction
This example dynamically demonstrates the geometric construction and properties of a parabola using GeoGebra. It involves core mathematical concepts such as the definition of a parabola, similarity transformation, coordinate geometry, and geometric construction. Key construction elements include commands and objects like Line, Point, Segment, OrthogonalLine, LineBisector, Intersect, Circle, Distance, CurveCartesian, and If. Suitable for high school and above learners to understand the geometric definition and transformation properties of parabolas.

GeoGebra Commands & Parameters

  1. Line(A_1, B) → p
  2. Point(p) → A
  3. Segment(A, F) → a
  4. OrthogonalLine(A, p) → b
  5. LineBisector(a) → c
  6. Intersect(b, c) → T
  7. Point(c) → K
  8. Segment(K, A) → e
  9. OrthogonalLine(K, p) → f
  10. Intersect(p, f) → C
  11. Segment(C, K) → g
  12. Segment(K, F) → j
  13. OrthogonalLine(F, p) → h
  14. Intersect(p, h) → O
  15. Circle(O, 1) → k
  16. Intersect(k, p, 1) → D
  17. Distance(O, F) → d
  18. CurveCartesian(x(O + (t * (D - O)) + ((t^(2) + d^(2)) / ((2 * d^(2))) * (F - O))), y(O + (t * (D - O)) + ((t^(2) + d^(2)) / ((2 * d^(2))) * (F - O))), t, -10, 10) → i
  19. Segment(T, F) → l
  20. If(ifo, "Hide", "Show") → text1