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Focus and Directrix of a Parabola

Focus and Directrix of a Parabola
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2020-04-02 05:30
Coordinate GeometryGeometric Construction
This example demonstrates the focus and directrix of a parabola and their geometric definition. Key math concepts include parabola, focus, directrix, and distance formulas. GeoGebra commands and objects used in construction are Line, Mirror, Segment, Intersect, CircleArc, OrthogonalLine, Angle, and Parabola. Suitable for high school students to learn and understand the geometric properties of parabolas, useful for teaching demonstrations and concept verification.

GeoGebra Commands & Parameters

  1. Line(C, V) → a
  2. Mirror(P, a) → P'
  3. Segment(P, P') → f
  4. Intersect(a, f) → A
  5. CircleArc(V, A, C) → c
  6. Intersect(c, a) → D, E
  7. Segment(E, P) → t_P
  8. Segment(E, P') → t_P'
  9. OrthogonalLine(V, a) → t_v
  10. Intersect(t_P, t_v) → F_1
  11. OrthogonalLine(F_1, t_P) → g
  12. Intersect(a, g) → F
  13. Segment(F_1, F) → h
  14. Angle(P, F_1, F) → α
  15. CircleArc(V, F, C) → d_1
  16. Intersect(d_1, a, 2) → B
  17. OrthogonalLine(B, a) → d
  18. Parabola(F, d) → e
  19. Mirror(V, F_1) → T_P
  20. Intersect(g, d) → D_P
  21. Segment(D_P, P) → i
  22. Segment(D_P, F_1) → j

AI Drawing Prompt Reference

Draw a parabola, highlighting its focus and directrix to demonstrate the geometric definition. Start by drawing a line and the vertex of the parabola, then mirror the line over the vertex to create a symmetrical line. Connect the vertex to the mirrored point to form the focus. Find the intersection points of the mirrored line with the parabola, and draw segments from these points to the vertex. Next, draw a perpendicular line from the vertex to the focus, and find the intersection point. Finally, draw a large circle centered at the vertex and focus, and find the intersection points with the directrix to complete the parabola.
The prompt above was compiled from the original drawing commands and is for reference only.