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Parabola by Locus Definition

Parabola by Locus Definition
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2012-03-08 04:19
Coordinate GeometryGeometric ConstructionLocusGraphing
This example demonstrates the locus definition of a parabola, where any point on the parabola is equidistant from the focus and the directrix line. Key math concepts include parabola, focus, directrix, and distance formula. Construction highlights the use of GeoGebra commands like Segment, LineBisector, OrthogonalLine, and Intersect, along with objects A, B, a, p, M, F, etc. Ideal for high school students learning analytical geometry.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(M, F) → b
  3. LineBisector(M, F) → c
  4. OrthogonalLine(M, a) → d
  5. Intersect(d, c) → P
  6. Segment(F, P) → FP
  7. Segment(P, M) → MP

AI Drawing Prompt Reference

Draw a parabola where any point on it is equidistant from focus F and line a. Start by plotting points A and B and connecting them to form line a. Then, take point M and set focus F, draw the perpendicular bisector of M and F to get line c. Next, draw the perpendicular from M to line a to get line d, and find the intersection P of d and c. Connect F and P to get line FP, and connect P and M to get line MP, forming part of the parabola.
The prompt above was compiled from the original drawing commands and is for reference only.