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Parabola as a Locus

Parabola as a Locus
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2018-09-04 08:57
FunctionCoordinate GeometryLocus
This example demonstrates the construction of a parabola as a locus. Key mathematical concepts include parabola, real numbers, and locus. Using GeoGebra commands such as Line, Point, OrthogonalLine, Segment, LineBisector, Intersect, and Angle, a parabola can be constructed. Suitable for high school mathematics education and learning coordinate geometry.

GeoGebra Commands & Parameters

  1. Line(B, C) → f
  2. Point(f) → D
  3. OrthogonalLine(D, f) → g
  4. Segment(A, D) → h
  5. LineBisector(h) → i
  6. Intersect(i, g) → E
  7. Segment(A, E) → j
  8. Angle(f, g) → α
  9. Segment(E, D) → k

AI Drawing Prompt Reference

Draw a horizontal line as the directrix, and place a fixed point above it as the focus. Pick an arbitrary point on the directrix and draw a perpendicular line through it. Connect the focus to this point, then construct the perpendicular bisector of that segment. The bisector intersects the perpendicular line at a new point. Connect the focus to this intersection, and also connect the intersection back to the point on the directrix. Finally, mark the angle between the directrix and the perpendicular line. This construction illustrates the parabola as a locus of points equidistant from the focus and directrix.
The prompt above was compiled from the original drawing commands and is for reference only.