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Generic Ellipses as Envelopes

Vincent J. Matsko
Mathematics Magazine
Vol. 86, No. 5 (December 2013), pp. 358-365
DOI: 10.4169/math.mag.86.5.358
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.86.5.358
Page Count: 7
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Generic Ellipses as Envelopes
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Abstract

Summary The astroid is well known as an envelope both of a family of line segments and a family of ellipses. The relationship between these two families is investigated by asking when two generic ellipses are tangent to each other, where a generic ellipse is described by \documentclass{article} \pagestyle{empty}\begin{document} $|x/a|^m+|y/b|^m=1$ \end{document} for some a, b, m > 0. Results are illustrated with several examples of envelopes of families of generic ellipses.

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