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Focus-Directrix Definition of an Ellipse by Norm Prokup

Focus-Directrix Definition of an Ellipse by Norm Prokup
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2017-02-22 03:58
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the focus-directrix definition of an ellipse, illustrating the geometric concept that the set of points equidistant from a focus and a directrix forms an ellipse. Key math concepts include ellipse definition, foci, directrices, and coordinate geometry. Construction involves GeoGebra commands like Point, Sequence, Segment, OrthogonalLine, Intersect, utilizing objects such as ε, λ, F, B, text elements, and lists. Suitable for high school students studying conic sections and geometric properties of ellipses, ideal for classroom instruction or interactive exploration.

GeoGebra Commands & Parameters

  1. Point(λ) → B
  2. Sequence((((4 * sqrt(1 - ε^(2))) * cos(t)), (4 * ε) + (4 * sin(t))), t, 0, (2 * π), π / 36) → list1
  3. Point(list1) → P
  4. Segment(F, P) → f
  5. OrthogonalLine(P, λ) → g
  6. Intersect(λ, g) → N
  7. Segment(P, N) → h