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Locus of a Parabola by ian.g.woods

Locus of a Parabola by ian.g.woods
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2016-10-24 11:13
VectorFunctionCoordinate GeometryLocus
This example demonstrates the locus definition of a parabola, showing the set of points equidistant from a fixed point (focus) and a fixed line (directrix). It involves core concepts like parabola definition, ratios, linear equations, and 2D vectors. Construction highlights the use of GeoGebra commands/objects such as Point, OrthogonalLine, Midpoint, Segment, Intersect, and Angle. Suitable for high school coordinate geometry teaching or exploration by math enthusiasts.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. OrthogonalLine(A, yAxis) → Directrix
  3. Point(Directrix) → C
  4. Midpoint(FOCUS, C) → D
  5. Segment(FOCUS, D) → g
  6. Segment(D, C) → h
  7. OrthogonalLine(C, Directrix) → i
  8. OrthogonalLine(D, g) → j
  9. Intersect(i, j) → P
  10. Segment(FOCUS, P) → k
  11. Segment(P, C) → l
  12. Segment(D, P) → m
  13. Angle(C, D, P) → α
  14. Angle(P, C, A) → β