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Parabola - Focus/Directrix Definition

Parabola - Focus/Directrix Definition
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2020-02-04 08:41
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the geometric definition of a parabola based on its focus and directrix, involving concepts like isosceles triangles and logarithmic functions. It constructs the parabola using GeoGebra commands such as Line, Parabola, Point, OrthogonalLine, Intersect, and Segment. Suitable for high school and advanced learners exploring coordinate geometry and parabolic properties.

GeoGebra Commands & Parameters

  1. Line(B, C) → a
  2. Parabola(A, a) → c
  3. Point(c) → D
  4. OrthogonalLine(D, a) → f
  5. Intersect(a, f) → E
  6. Segment(E, D) → g
  7. Segment(D, A) → h

AI Drawing Prompt Reference

Draw a parabola demonstrating its geometric definition using a focus and directrix. Start by plotting a line through the focus and directrix, then sketch the parabola based on this line and the focus. Take a point on the parabola, draw a perpendicular line from this point to the directrix, and find their intersection. Connect this intersection to the point on the parabola, and also connect the point on the parabola to the focus to illustrate the construction and key geometric relationships.
The prompt above was compiled from the original drawing commands and is for reference only.