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Conics as Envelopes of Straight Lines

Conics as Envelopes of Straight Lines
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2019-03-19 17:53
CircleCoordinate GeometryGeometric Construction
This example demonstrates how ellipses and hyperbolas can be seen as envelopes of straight lines. Key mathematical concepts include the relationship between lines and curves in coordinate geometry. Using GeoGebra commands such as Sequence, Length, Element, and Circle, dynamic constructions of these curves are possible. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence(LineBisector[(cos(i), sin(i)), A], i, 0, (2 * π), π / 20) → Lines
  2. Length(Lines) → Lng
  3. Sequence(Element[Lines, i], i, 1, n) → Partial
  4. Sequence((cos(i), sin(i)), i, 0, (2 * π), π / 20) → PointsCircle
  5. Element(PointsCircle, n) → B
  6. Circle(O, 1) → c