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Locus of a Parabola by Frederick HO

Locus of a Parabola by Frederick HO
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2014-06-25 17:11
TrigonometryCoordinate Geometry
This example demonstrates the construction of a parabola's locus. It involves core mathematical concepts such as parabolas, power functions, division, geometric mean, circles, and trigonometry. The construction utilizes GeoGebra commands/objects like Point, Segment, LineBisector, OrthogonalLine, Intersect, Locus, and Angle. It is suitable for high school students studying coordinate geometry.

GeoGebra Commands & Parameters

  1. Point(d) → V
  2. Segment(V, F) → b
  3. LineBisector(b) → c
  4. OrthogonalLine(V, d) → d_1
  5. Intersect(c, d_1) → P
  6. Locus(P, V) → loc1
  7. Segment(F, P) → e
  8. Segment(V, P) → f
  9. Angle(f, d) → α
  10. Angle(c, b) → β

AI Drawing Prompt Reference

Draw a line segment with a point at one end. Construct the perpendicular bisector of the segment. From the other end of the segment, draw a perpendicular line to the bisector and mark their intersection. Trace the path of the intersection point as the other endpoint moves, forming a parabola. Show the segment, bisector, perpendicular line, and the traced path, and label the angle between the segment and the perpendicular line, as well as the angle between the bisector and the segment.
The prompt above was compiled from the original drawing commands and is for reference only.