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Parabola as Geometric Locus

Parabola as Geometric Locus
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2020-02-25 19:42
FunctionCoordinate GeometryGeometric Construction
This example demonstrates how to construct a parabola as a geometric locus. Key mathematical concepts include the definition and properties of a parabola. Construction highlights include the use of points, orthogonal lines, intersections, circles, and segments in GeoGebra.

GeoGebra Commands & Parameters

  1. Parabola(Fuoco, Direttrice) → d
  2. Point(d) → M
  3. OrthogonalLine(M, Direttrice) → e
  4. Intersect(Direttrice, e) → C
  5. Circle(M, Segment[M, C]) → f
  6. Segment(M, C) → g
  7. Segment(M, Fuoco) → h

AI Drawing Prompt Reference

Draw a parabola with a given focus and directrix. Start by picking a point on the directrix, then draw a perpendicular line from this point to the directrix, and find the intersection of this perpendicular line with the directrix, which is the vertex. Draw a circle with the vertex as the center and the distance between the vertex and the focus as the radius. The intersection of this circle with the perpendicular line gives a point on the parabola. Connect the vertex to this point and to the focus to form part of the parabola.
The prompt above was compiled from the original drawing commands and is for reference only.