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Focus-Directrix Parabola by morjoh86

Focus-Directrix Parabola by morjoh86
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2019-04-03 16:41
FunctionCoordinate GeometryGeometric Construction
This example demonstrates a parabola defined by its focus and directrix. Key mathematical concepts include the geometric properties of parabolas and coordinate geometry. Using GeoGebra commands such as Line, OrthogonalLine, Intersect, Segment, Midpoint, Point, and Angle, the focus, directrix, vertex, and other key elements of the parabola can be constructed. Suitable for high school mathematics education, particularly for teaching and learning about parabolas in coordinate geometry.

GeoGebra Commands & Parameters

  1. Line(A, B) → DIRECTRIX
  2. OrthogonalLine(Focus, DIRECTRIX) → a
  3. Intersect(a, DIRECTRIX) → C
  4. Segment(Focus, C) → e
  5. Midpoint(Focus, C) → VERTEX
  6. Point(f) → D
  7. OrthogonalLine(D, DIRECTRIX) → b
  8. Intersect(b, DIRECTRIX) → E
  9. Segment(D, E) → c
  10. Segment(Focus, D) → d
  11. Angle(D, E, A) → α

AI Drawing Prompt Reference

Draw a parabola with focus F and directrix L. First, draw the directrix L, then draw a perpendicular line a from F to L, find the intersection C of a and L, and connect FC to get segment e, with C being the vertex V of the parabola. Next, draw a perpendicular line b from F to L, find the intersection E of b and L, and connect DE to get segment c. Then, draw a perpendicular line f from D to L, find the intersection D of f and L, and connect FD to get segment d. Finally, measure angle α between D, E, and A.
The prompt above was compiled from the original drawing commands and is for reference only.