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Vertical Hyperbola Demo

Vertical Hyperbola Demo
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2017-08-01 03:14
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the geometric properties and algebraic characteristics of a vertical hyperbola. Key concepts include the definition of a hyperbola, foci, asymptotes, eccentricity, vertices, real and imaginary axes. Construction highlights involve using commands like Point, Segment, Intersect, OrthogonalLine to draw the hyperbola, foci, vertices, asymptotes, and distances from foci to points. Suitable for high school coordinate geometry education and learning to understand the geometric construction and parameter significance of hyperbolas.

GeoGebra Commands & Parameters

  1. Point(Hyperbola) → P_1
  2. Segment(F_t, P_1) → dl_1
  3. Segment(P_1, F_b) → dl_2
  4. Point(Hyperbola) → P_2
  5. Segment(P_2, F_b) → dr_1
  6. Segment(P_2, F_t) → dr_2
  7. Segment(F_t, F_b) → d
  8. Intersect(Hyperbola, d) → A, B
  9. OrthogonalLine(F_t, d) → e
  10. OrthogonalLine(A, d) → f
  11. OrthogonalLine(B, d) → g
  12. OrthogonalLine(F_b, d) → i
  13. Intersect(Hyperbola, e) → C, D
  14. Intersect(f, Asymp_2) → E
  15. Intersect(f, Asymp_1) → F
  16. Intersect(Hyperbola, i) → G, H
  17. Intersect(Asymp_1, g) → I
  18. Intersect(g, Asymp_2) → J
  19. Segment(D, C) → LR_t
  20. Segment(H, G) → LR_b
  21. Segment(E, F) → j
  22. Segment(F, J) → l
  23. Segment(J, I) → m
  24. Segment(I, E) → n

AI Drawing Prompt Reference

Draw a vertical hyperbola, marking its foci, vertices, real and imaginary axes. Plot the segment between the foci and find its intersections with the hyperbola. Draw lines from the foci perpendicular to this segment, and locate their intersections with the hyperbola. Connect these intersection points to form the asymptotes, and label the distances between key points.
The prompt above was compiled from the original drawing commands and is for reference only.