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Equations of Ellipses

Equations of Ellipses
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2016-07-29 03:59
FunctionCoordinate GeometryGeometric ConstructionSlider AnimationLocus
This example demonstrates the standard equations of ellipses and their geometric significance. Key math concepts include the definition of an ellipse, standard equations, focal distance, and directrices. GeoGebra commands/objects used in construction are If statements, Points, and Segments. Suitable for high school students learning the connection between geometric properties and algebraic expressions of ellipses.

GeoGebra Commands & Parameters

  1. If(a ≠ b, If[a > b, (x(C) - f_1, y(C)), (x(C), y(C) + f_1)]) → F_1
  2. If(a ≠ b, If[a ≥ b, (x(C) + f_1, y(C)), (x(C), y(C) - f_1)]) → F_2
  3. Point(c) → P
  4. If(a ≠ b, If[a ≥ b, (x(C) - a, y(C)), (x(C), y(C) + b)]) → V_1
  5. If(a ≠ b, If[a ≥ b, (x(C) + a, y(C)), (x(C), y(C) - b)]) → V_2
  6. Segment(If[a ≠ b, F_1, C], P) → d_1
  7. Segment(P, If[a ≠ b, F_2, C]) → d_2
  8. Segment(C, F_2) → f
  9. Segment(C, V_1) → d