Conic Sections Defined by Eccentricity

Conic Sections Defined by Eccentricity
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2018-05-01 01:32
This example demonstrates how conic sections (ellipse, parabola, hyperbola) are defined by their eccentricity dynamically. Key math concepts include eccentricity, conic section definitions, and analytical geometry. Construction involves commands like Point, Circle, Line, Intersect, OrthogonalLine, Segment, Angle, CircleArc, If, and objects such as F, excentricity, x0, y0, etc. Suitable for high school and above students to explore the properties and classification of conic sections.

GeoGebra Commands & Parameters

  1. Point(c) → P
  2. Circle(P, F) → d
  3. Line(P, kierownica) → a
  4. Intersect(d, a) → B, M
  5. OrthogonalLine(P, kierownica) → b
  6. Intersect(kierownica, b) → P'
  7. Segment(P', M) → e
  8. Segment(P, M) → f
  9. Segment(P, P') → g
  10. Segment(P, F) → h
  11. Angle(M, P', P) → α
  12. CircleArc(P, F, M) → k
  13. If(excentricity < 1, "Ellipse", If[excentricity ≟ 1, "Parabola", "Hyperbola"]) → nazwa