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Focus and Directrix Determine a Parabola

Focus and Directrix Determine a Parabola
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2016-01-02 23:53
Coordinate GeometryGeometric Construction
This example visually demonstrates how a focus and a directrix determine a parabola. It involves core math concepts like the definition of a parabola, coordinate geometry, and geometric constructions. Key GeoGebra commands and objects used include Line, OrthogonalLine, Intersect, Segment, Midpoint, Point, and Angle. Suitable for high school and above students to understand the geometric definition and properties of parabolas.

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