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Focus and Directrix Determine a Parabola by Terry Lee Lindenmuth

Focus and Directrix Determine a Parabola by Terry Lee Lindenmuth
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2015-02-10 06:16
Coordinate GeometryGeometric Construction
This example visually demonstrates how a parabola is determined by a focus and a directrix. It involves core mathematical concepts such as the definition of a parabola, coordinate geometry, and geometric construction. The construction utilizes GeoGebra commands and objects like Line, OrthogonalLine, Intersect, Segment, Midpoint, Point, and Angle. It is suitable for high school students and above to learn and understand the geometric definition and applications 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

AI Drawing Prompt Reference

Draw a parabola determined by a focus and a directrix. First, draw the directrix, then draw a line perpendicular to the directrix through the focus, and find the intersection point C on the directrix. Connect the focus and point C, and find the midpoint as the vertex. Then, take a point D on the directrix, draw a line perpendicular to the directrix through point D, and find the intersection point E. Connect points D and E, connect the focus and point D, and finally measure the angle DEA.
The prompt above was compiled from the original drawing commands and is for reference only.