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Ellipse with Concentric Circles by Chip Rollinson

Ellipse with Concentric Circles by Chip Rollinson
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2016-02-21 12:59
CircleTrigonometryCoordinate GeometryTransformationLocus
In collections Conic Section Collection
This dynamic example illustrates the geometric relationship between an ellipse and concentric circles, generated by rotating circles and tracing their intersection points. Core mathematical concepts include the ellipse definition, circular rotation transformations, locus theory, and vector geometry. Construction heavily utilizes GeoGebra commands such as Intersect, Circle, Rotate, and Locus, with dynamic control of circle radii r₁, r₂ and points A, B, C. It is suitable for high school geometry, analytic geometry, or trigonometry units, helping learners intuitively grasp ellipse construction and parameter variation.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, r_1) → c
  3. Circle(A, r_2) → d
  4. Rotate(B, e, A) → B'
  5. Rotate(C, (-e), A) → C'
  6. Segment(B', C') → f
  7. Midpoint(f) → D
  8. Locus(D, e) → loc1
  9. Segment(D, B') → g
  10. Segment(C', D) → h