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Parabola - Equidistant from Focus and Directrix

Parabola - Equidistant from Focus and Directrix
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2016-04-27 18:55
FunctionCoordinate GeometryGeometric Construction
This example illustrates the definition of a parabola, where the distance from any point on the parabola to the focus is equal to the distance to the directrix. Key mathematical concepts include parabolas, distance, and geometric construction. The commands used include Line, Point, OrthogonalLine, Segment, Midpoint, Intersect, and Distance. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(A, B) → Directrix
  2. Point(Directrix) → C
  3. OrthogonalLine(C, Directrix) → b
  4. Segment(Focus, C) → c
  5. Midpoint(C, Focus) → E
  6. OrthogonalLine(E, c) → d
  7. Intersect(d, b) → Parabola
  8. Segment(Focus, Parabola) → DistancePF
  9. Distance(Parabola, Focus) → a
  10. Distance(C, Parabola) → DistanceDP
  11. Segment(Parabola, C) → DistancePD

AI Drawing Prompt Reference

Draw a parabola where the distance from any point on the parabola to the focus is equal to the distance to the directrix. Start by drawing a line as the directrix, then take a point C on the line and draw a perpendicular line b from C to the directrix. Connect the focus to C, find the midpoint E, and draw a perpendicular line d from E to the focus line. The intersection of d and b is a point on the parabola, and the segment connecting the focus to this point represents the distance from the focus to the parabola.
The prompt above was compiled from the original drawing commands and is for reference only.