Reflection across a Parabola

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2017-02-18 10:19

This example demonstrates the reflection of a point across a parabola. Key math concepts include parabola, reflection, focus, directrix, etc. Construction highlights the use of GeoGebra commands like Parabola, Segment, Point, Tangent, OrthogonalLine, Intersect, Circle, and Textfield. Suitable for high school and above students to understand the geometric properties and reflection principles of parabolas.

GeoGebra Commands & Parameters

Parabola(Focus, f) → c
Segment(B, A) → g
Point(c) → P
Tangent(P, c) → h,
OrthogonalLine(P, h) → i
Intersect(i, g) → M
Circle(P, M) → d
Intersect(d, i, 2) → M'
Segment(M', P) → j
Segment(M, P) → k
Circle(C, r) → e
Intersect(e, i) → E, D
Circle(P, D) → p
Intersect(p, i, 2) → D'
Circle(P, E) → q
Intersect(q, i, 2) → E'
Segment(E, P) → l
Segment(E', P) → m
Segment(E, D') → n
Textfield(r) → InputBox1