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Ellipse Definition, Equation, and Transformations

Ellipse Definition, Equation, and Transformations
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2015-11-06 07:18
Coordinate GeometryTransformationLocusGraphing
This GeoGebra applet demonstrates the definition of an ellipse and its standard equation through dynamic transformations. Key concepts include foci, eccentricity, major and minor axes, and coordinate shifts. Construction utilizes points, segments, and conditional commands with parameters a, b, h, k to visualize the locus. Ideal for high school geometry classes or calculus preparation.

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_1) → 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) → c
  9. Segment(C, V_1) → d