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Definition of a Parabola

Definition of a Parabola
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2015-10-03 05:09
Coordinate GeometryGeometric Construction
This example illustrates the definition of a parabola. Key mathematical concepts include the geometric properties and construction methods of parabolas. Using GeoGebra commands such as Line, Parabola, Point, etc., the generation process of the parabola is visually demonstrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Parabola(C, a) → c
  3. Point(a) → F
  4. OrthogonalLine(F, a) → b
  5. Segment(F, C) → g
  6. Midpoint(g) → G
  7. OrthogonalLine(G, g) → h
  8. Intersect(h, b) → H
  9. Segment(C, H) → i
  10. Segment(F, H) → j
  11. Angle(j, a) → α
  12. OrthogonalLine(H, h) → d
  13. Circle(H, C) → f

AI Drawing Prompt Reference

Draw a parabola with focus C and directrix a. First, draw line a, then create parabola c using C and a as parameters. Next, take point F on line a and draw its perpendicular line b. Connect F and C to form segment g, find the midpoint G of g, draw its perpendicular line h, and find the intersection H of h and b. Draw segments CH and FH to form i and j, measure the angle between j and a as α, and draw the perpendicular line d from H. Finally, draw a circle with center H and radius C.
The prompt above was compiled from the original drawing commands and is for reference only.