Parabolic Envelope from Congruent Triangles

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Consider a line and a point not on . Drag the orange point along . Draw a vertical line from . The perpendicular bisector of meets at a point that traces out a parabola and is tangent to the parabola. The focus and directrix of the parabola are and because is isoceles. The part of the vertical line m inside the parabola is the reflection in of the ray .

Contributed by: Harry Calkins (March 2011)
Open content licensed under CC BY-NC-SA


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