MathPlotAI Logo MathPlotAI

Parabola as a Locus of Points

Parabola as a Locus of Points
Loading the math board and drawing, please wait…
2015-06-17 21:10
Coordinate GeometryLocus
This example demonstrates a parabola as the locus of points equidistant from a point (focus) and a line (directrix). Key concepts include the definition of a parabola, construction methods, and the use of GeoGebra commands such as Line, Circle, OrthogonalLine, Intersect, etc. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(B, C) → a
  2. Circle(Focus, Dist) → c
  3. OrthogonalLine(Focus, a) → b
  4. Intersect(b, a) → D
  5. Midpoint(Focus, D) → E
  6. Intersect(c, b) → F, G
  7. Circle(D, Dist) → d
  8. Intersect(d, b) → H, I
  9. Line(I, a) → e
  10. Intersect(c, e) → J, K
  11. OrthogonalLine(J, a) → f
  12. OrthogonalLine(K, a) → g
  13. Segment(J, Focus) → h
  14. Segment(K, Focus) → i
  15. Locus(K, Dist) → loc1
  16. Locus(J, Dist) → loc2
  17. Intersect(f, a) → L
  18. Intersect(g, a) → M
  19. Segment(L, J) → j
  20. Segment(K, M) → k
  21. Segment(L, M) → l
  22. Segment(L, M) → m
  23. Segment(M, L) → n
  24. Segment(L, M) → p

AI Drawing Prompt Reference

Draw a parabola, which is the set of points equidistant from a focus F and a direct line L. First, draw the direct line L and the focus F. Then, construct a line M perpendicular to L, and find its intersection D with L. Next, construct a circle c with D as the center. Then, construct a line N perpendicular to F through D, and find its intersections E and F with circle c. Construct a circle d with E as the center, and find its intersections H and I with line N. Construct lines O and S perpendicular to L through I and K, and find their intersections J and K with circle c. Finally, construct line segments p and q from J and K to F, and lines r and s perpendicular to L through J and K, and construct the locus loc1 and loc2 of J and K.
The prompt above was compiled from the original drawing commands and is for reference only.