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Constant Length of the Projection of the Normal of a Parabola

Constant Length of the Projection of the Normal of a Parabola
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2017-05-13 00:19
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the constant length of the projection of the normal of a parabola. Key mathematical concepts include parabolas, functions, and geometric transformations. Using GeoGebra commands such as Intersect, Point, Mirror, Tangent, and OrthogonalLine, the construction of the parabola and its normal is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(c, j, 1) → K
  2. Point(j) → L
  3. Mirror(L, K) → G
  4. Tangent(L, c) → f, g
  5. Intersect(c, g) → E
  6. OrthogonalLine(E, g) → h
  7. Intersect(j, h) → R
  8. Line(E, G) → i
  9. Intersect(c, i, 2) → H
  10. Focus(c) → F,
  11. Segment(E, F) → k
  12. Angle(L, E, R) → α
  13. Angle(E, G, R) → β