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Eccentricity and Directrix of an Ellipse

Eccentricity and Directrix of an Ellipse
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2017-03-03 00:22
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the geometric relationship between the eccentricity and directrix of an ellipse. Key math concepts include ellipse definition, eccentricity, directrix, and coordinate geometry. Construction highlights involve GeoGebra commands like OrthogonalLine, Point, Ellipse, Distance, Segment, and Intersect. Suitable for high school coordinate geometry instruction or student exploration.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A, xAxis) → Δ_2
  2. Point(xAxis) → F_2
  3. Point(xAxis) → F_1
  4. Point(yAxis) → B_2
  5. Ellipse(F_2, F_1, B_2) → c
  6. Point(c) → M
  7. Distance(M, F_2) → distanceEB
  8. Segment(M, F_2) → b
  9. OrthogonalLine(M, Δ_2) → d_1
  10. Intersect(Δ_2, d_1) → H
  11. Segment(M, H) → e
  12. Distance(M, H) → distanceEH
  13. OrthogonalLine(F, xAxis) → Δ_1
  14. Intersect(c, xAxis, 2) → A_2
  15. Intersect(c, xAxis, 1) → A_1

AI Drawing Prompt Reference

Draw an ellipse with two foci F1 and F2 on the x-axis and a vertex B2 on the y-axis. Calculate the distance from a point M on the ellipse to focus F2 (distanceEB) and the distance from M to the x-axis (distanceEH). Draw a perpendicular line from M to the x-axis, and find the intersection H with the perpendicular line from M to the line segment A1A2, then draw the line segment e from M to H.
The prompt above was compiled from the original drawing commands and is for reference only.