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Circles & Ellipses in the {Radius, Eccentricity} Plane

Circles & Ellipses in the {Radius, Eccentricity} Plane
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2017-07-31 22:36
CircleVectorCoordinate GeometryOptimization
This example demonstrates how circles and ellipses are represented in the {radius, eccentricity} parameter space. Key math concepts include circle, ellipse, eccentricity, coordinate geometry, and vector. It uses GeoGebra commands like Point, Ellipse, Intersect, Min, Max, Circle, Vector, Ray, AxisStepX for construction. Suitable for high school students and educators to explore parametric representations and geometric properties of conic sections.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(yAxis) → B
  3. Ellipse(B, B', A) → d
  4. Intersect(d, yAxis) → E, F
  5. Min(abs(y(F)), abs(x(A))) → minor
  6. Max(abs(y(F)), abs(x(A))) → major
  7. Circle((0, 0), x(A)) → c
  8. Vector(C, A) → u
  9. Vector(C, B) → v
  10. Ray((0, 1), (1, 1)) → f
  11. AxisStepX() → a