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Parabola Locus and Similarity Transformation

Parabola Locus and Similarity Transformation
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2018-01-28 15:17
Coordinate GeometryLocus
This example demonstrates the generation of a parabola's locus and its similarity transformation effects. Key math concepts include parabola definition, similarity transformation, quadratic equations, algebra, and geometric transformations. Construction highlights GeoGebra commands like Intersect, Line, Segment, Focus, Midpoint, and If. Suitable for high school and above learners to understand parabola geometry and transformation applications.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, xAxis) → O
  2. Line(A, xAxis) → d
  3. Segment(A, O) → b_1
  4. Focus(c) → E,
  5. Line(E, b_1) → e
  6. Intersect(d, e) → B
  7. Segment(A, B) → f
  8. Segment(B, E) → g
  9. Segment(B, O) → h
  10. Segment(A, E) → i
  11. Midpoint(A, E) → M
  12. If(a ∨ b, 1, 0) → speed

AI Drawing Prompt Reference

Draw a parabola with its vertex at the origin, using point A and focus E to construct the directrix line d and the line e through focus E. Find the intersection point B of line d and line e, then connect points A, B, E, and the origin O with line segments to demonstrate the geometric properties and similarity transformations of the parabola.
The prompt above was compiled from the original drawing commands and is for reference only.