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Ellipse from Definition and Transformations

Ellipse from Definition and Transformations
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2015-11-06 23:07
VectorTransformation
This example demonstrates how to draw an ellipse based on its definition and apply transformations. Key mathematical concepts include the definition of an ellipse, graphical transformations, and vectors. Using GeoGebra commands such as If, Point, and Segment, the construction process is dynamically illustrated. Suitable for high school mathematics education and learning.

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