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Parabola Locus Demonstration

Parabola Locus Demonstration
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2018-04-23 14:12
Coordinate GeometryGeometric Construction
This example demonstrates the formation and properties of a parabola locus. It involves core mathematical concepts such as the definition of a parabola, median value, logarithm, isosceles triangles, orthocenter, and logical reasoning. The construction uses GeoGebra commands like Point, Distance, Segment, and Angle to create key objects F, c, P, FP, LHS, RHS, O, and α. It is suitable for high school and above students to understand the dynamic changes and geometric relationships of the parabola locus.

GeoGebra Commands & Parameters

  1. Point(c) → P
  2. Distance(F, P) → FP
  3. Segment(F, P) → LHS
  4. Segment(P, A) → RHS
  5. Angle(P, A, O) → α

AI Drawing Prompt Reference

Draw a parabola locus demonstration showing point F and point P, where the distance from P to F equals the distance from P to a fixed line, illustrating the definition of a parabola. Include segment from P to A, angle at P formed by points P, A, and O, and segments from F to P (LHS) and P to A (RHS) to highlight geometric properties and dynamic relationships.
The prompt above was compiled from the original drawing commands and is for reference only.