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Parabola as Envelope of Straight Lines

Parabola as Envelope of Straight Lines
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2019-03-19 17:52
Coordinate GeometryGeometric Construction
This example demonstrates a parabola as the envelope of a family of straight lines. Key mathematical concepts include the theory of envelopes in coordinate geometry. Using GeoGebra commands such as Line, Sequence, Length, and Element, a dynamic construction of the parabola is achieved. Suitable for high school mathematics education, particularly in coordinate geometry and curve sketching.

GeoGebra Commands & Parameters

  1. Line((0, 0), (1, 0)) → l
  2. Sequence(LineBisector[(i, 0), B], i, -3, 3, 1 / 10) → Lines
  3. Length(Lines) → lng
  4. Sequence(Element[Lines, i], i, 1, n) → PartialLines
  5. Sequence((i, 0), i, -3, 3, 1 / 10) → PointsA
  6. Element(PointsA, n) → A