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Parabola (Locus Construction)

Parabola (Locus Construction)
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2015-07-11 02:14
FunctionCoordinate GeometryGeometric Construction
In collections CCSS High School: Geometric Properties of Parabola
This GeoGebra applet demonstrates how a parabola is defined as the locus of points in the plane that are equidistant from a fixed point. It involves key mathematical concepts such as geometric construction, locus, and coordinate geometry. Using GeoGebra commands like Line, Point, OrthogonalLine, Segment, LineBisector, etc., the generation process of the parabola can be visually understood. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(A, B) → d
  2. Point(d) → D
  3. OrthogonalLine(D, d) → b
  4. Segment(D, F) → c
  5. LineBisector(c) → a
  6. Angle(c, a) → α
  7. Intersect(b, a) → P
  8. Segment(P, F) → d_1
  9. Segment(D, P) → e
  10. Intersect(a, c) → C
  11. Segment(D, C) → f
  12. Segment(C, F) → g
  13. Angle(d, e) → β

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 construct a perpendicular line through it. Connect this point to the focus, then draw the perpendicular bisector of that segment. The intersection of the bisector and the perpendicular line gives a moving point. Connect this moving point to both the focus and the directrix point, and mark the relevant angles. As the directrix point moves, the locus of the moving point traces a parabola, maintaining equal distances to the focus and the directrix.
The prompt above was compiled from the original drawing commands and is for reference only.