MathPlotAI Logo MathPlotAI

Vertical Hyperbola by hgraber26

Vertical Hyperbola by hgraber26
Loading the math board and drawing, please wait…
2018-02-24 01:14
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the geometric construction of a vertical hyperbola. Key mathematical concepts include the definition of a hyperbola, foci, and asymptotes. Using GeoGebra commands such as Focus, Point, Segment, and Asymptote, the properties of the hyperbola can be dynamically illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Focus(c_2) → F_2, F_1
  2. Point(c_2) → M_1
  3. Segment(F_1, M_1) → d_1
  4. Segment(F_2, M_1) → d_2
  5. Point(c_2) → M_2
  6. Segment(F_2, M_2) → d_4
  7. Segment(M_2, F_1) → d_3
  8. Asymptote(c_2) → i, j
  9. Intersect(j, i) → F
  10. Center(Hyperbola[F_2, F_1, b]) → Center
  11. Vertex(Hyperbola[F_2, F_1, a]) → V_2, V_1, ,
  12. OrthogonalLine(B, xAxis) → e
  13. OrthogonalLine(A, xAxis) → f
  14. Line(V_1, xAxis) → g
  15. Line(V_2, xAxis) → l
  16. Intersect(e, g) → C
  17. Intersect(f, g) → D
  18. Intersect(f, l) → E
  19. Intersect(e, l) → G
  20. Polygon(C, D, E, G) → poly1, c_1, d_6, e_1, g_1
  21. Segment(Center, V_1) → a_1
  22. Segment(V_1, C) → b_1
  23. Circle(Center, F_1) → p
  24. Point(p) → H
  25. Segment(Center, H) → m
  26. Intersect(c_1, b_1) → I
  27. Intersect(g_1, c_1) → J
  28. Segment(Center, J) → c
  29. Segment(Center, H) → n

AI Drawing Prompt Reference

Draw a vertical hyperbola with foci F1 and F2, asymptotes i and j, vertices V1 and V2, center, and a polygon constructed from these elements. Start by defining the foci and vertices, then draw the asymptotes, construct the center and vertices, and finally use these elements to draw the hyperbola and polygon.
The prompt above was compiled from the original drawing commands and is for reference only.