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Parabola Recursion

Topic:
Parabola
Orange is the locus of all points equidistant from the orange point and the red line-- a parabola. Yellow is the locus of all points equidistant form the yellow point and the orange parabola-- a parabola of a parabola...
Are there places where all four segments are equal? Twitter @farrarscott www.scottfarrar.com