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Locus Problem: Parabola Construction

Locus Problem: Parabola Construction
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2018-04-26 17:25
FunctionCoordinate GeometryLocus
In collections GCSE Higher Ch8 Transformations & Constructions
This example demonstrates how to construct the locus of a parabola using GeoGebra. Key mathematical concepts include the properties and construction methods of parabolas. Commands used include Line, OrthogonalLine, Intersect, Midpoint, Point, LineBisector, and Parabola. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(A, B) → d
  2. OrthogonalLine(F, d) → g
  3. Intersect(d, g) → D_1
  4. Midpoint(F, D_1) → E
  5. Point(d) → D
  6. LineBisector(D, F) → h
  7. Line(D, g) → i
  8. Intersect(h, i) → G
  9. Parabola(F, d) → c

AI Drawing Prompt Reference

Draw a parabola with focus F. First, draw a line d through points A and B, then draw the perpendicular line g to d. Find the intersection D1 of d and g, take the midpoint E of F and D1. Next, pick a point D on the line, draw the perpendicular bisector h of D and F, then draw the line i through D and g. Find the intersection G of h and i, and finally draw the parabola c with F and d as parameters.
The prompt above was compiled from the original drawing commands and is for reference only.