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Hyperbola with a Circle Locus

Hyperbola with a Circle Locus
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2015-03-05 11:01
CircleLocus
In collections Conic Section Collection
This example demonstrates the relationship between a hyperbola and a circle locus. Key mathematical concepts include hyperbolas, circles, and loci. Using GeoGebra commands such as Circle, Point, Segment, Line, LineBisector, Intersect, Angle, and Locus, a dynamic graphical representation of the hyperbola and circle locus is constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Circle(O, B) → c
  2. Point(c) → C
  3. Segment(O, C) → a
  4. Line(O, C) → b
  5. Segment(F, C) → d
  6. LineBisector(d) → e
  7. Intersect(e, d) → D
  8. Intersect(b, e) → L
  9. Angle(L, D, C) → α
  10. Segment(C, D) → f
  11. Segment(D, F) → g
  12. Locus(L, C) → loc1

AI Drawing Prompt Reference

Draw a hyperbola and construct a circle with center C by moving point C on circle c. Connect point O and C, and make line b. Construct segment OC and CF, find the perpendicular bisector e of OC, find the intersection D of e and d, find the intersection L of b and e, calculate angle α, connect CD and DF, and finally find the locus loc1 of point L on circle c.
The prompt above was compiled from the original drawing commands and is for reference only.