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Problem of the Week 1105

Locus of the Focus

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Take the standard parabola y = x2 with focus at (0, 1/4). If this parabola rolls without slipping along the x-axis, what is the locus of the focus?

Source: James Eels, The surfaces of Delaunay, The Mathematical Intelligencer 9:1 (1987) 53-57; and the book How Round Is Your Circle? by Bryant and Sangwin.

© Copyright 2008 Stan Wagon. Reproduced with permission.

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3 October 2008