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Drawing an Ellipse by Jennifer Silverman

Drawing an Ellipse by Jennifer Silverman
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2013-05-18 12:13
Coordinate GeometryGeometric Construction
In collections Exploring Conic Sections Drawing Conic Sections Exploring Conic Sections
This example demonstrates how an ellipse is constructed, involving core mathematical concepts like circles, intersections, lines, and midpoints. It utilizes GeoGebra commands and objects such as Circle, Intersect, Ellipse, Line, Point, Segment, Midpoint, OrthogonalLine, and Distance. Suitable for high school students learning about the definition and properties of ellipses.

GeoGebra Commands & Parameters

  1. Circle(A, g) → h
  2. Circle(B, e) → k
  3. Intersect(h, k, 1) → C_1
  4. Ellipse(A, B, C_1) → p
  5. Line(A, B) → i
  6. Point(p) → B'
  7. Segment(A, B') → s_1
  8. Segment(B, B') → s_2
  9. Segment(A, B) → a_1
  10. Midpoint(a_1) → G
  11. OrthogonalLine(G, a_1) → b_1
  12. Intersect(p, b_1) → F, E
  13. Line(A, B) → c
  14. Intersect(p, c) → C, D
  15. Segment(E, F) → d
  16. Segment(C, D) → f
  17. Distance(G, D) → distanceGD
  18. Distance(G, E) → distanceGE
  19. Segment(G, E) → b
  20. Segment(G, D) → a

AI Drawing Prompt Reference

Draw an ellipse by first creating two intersecting circles and identifying their intersection points. Then, form the ellipse using the centers of these circles and one intersection point. Next, connect the centers and find the midpoint, draw a perpendicular line from this midpoint to the connecting line, and mark where it intersects the ellipse. Connect these intersection points to the centers and measure the distances from the midpoint to each intersection point.
The prompt above was compiled from the original drawing commands and is for reference only.