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Tangents from an External Point to a Parabola

Tangents from an External Point to a Parabola
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2015-06-21 01:34
FunctionCoordinate GeometryGeometric Construction
In collections Conics Doug Kuhlmann
This example demonstrates how to construct tangents from an external point to a parabola. Key mathematical concepts include the properties of parabolas and the definition of tangents. Using GeoGebra commands such as Parabola, Intersect, and OrthogonalLine, the construction of tangents from a given point to the parabola is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Parabola(F, d) → c
  2. Circle(A, F) → e
  3. Intersect(e, d) → B, C
  4. OrthogonalLine(C, d) → a
  5. Intersect(c, a) → D,
  6. Line(A, D) → b
  7. OrthogonalLine(B, d) → f
  8. Intersect(c, f, 1) → E
  9. Line(A, E) → g
  10. Segment(F, A) → h
  11. Segment(A, C) → i
  12. Segment(A, B) → j
  13. Segment(F, E) → k
  14. Segment(F, D) → l

AI Drawing Prompt Reference

Draw a parabola and then draw two tangents from a point outside the parabola. First, draw a parabola with a focus and a directrix. Then, draw a circle with a point outside the parabola as the center and the directrix as the radius. Find the intersection points of the circle and the directrix. Draw two perpendicular lines from these intersection points to the parabola. The intersection points of these perpendicular lines with the parabola are the points of tangency. Connect these points and the point outside the parabola to get the two tangents.
The prompt above was compiled from the original drawing commands and is for reference only.