MathPlotAI Logo MathPlotAI

Parabola with Directrix, Focus, and Vertex

Parabola with Directrix, Focus, and Vertex
Loading the math board and drawing, please wait…
2015-10-22 00:42
VectorFunctionCoordinate GeometryGeometric Construction
This example demonstrates the geometric relationship between a parabola, its focus, directrix, and vertex. Key math concepts include parabola, vectors, linear regression, triangles, and coordinate geometry. Construction highlights involve commands like Line, Parabola, Mirror, Segment, Intersect, Distance, AreCongruent, and Prove in GeoGebra. Suitable for high school and above students studying parabolic properties and geometric constructions.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Parabola(C, a) → c
  3. Mirror(C, a) → C'
  4. Segment(C, C') → b
  5. Intersect(a, b) → D
  6. Intersect(c, b) → E,
  7. Distance(C, E) → CE
  8. Distance(E, D) → ED
  9. AreCongruent(CE, ED) →
  10. Segment(C, E) → f
  11. Segment(E, D) → g
  12. Prove(AreCongruent[f, g]) → d