Osculating Circle of Lemniscate of Gerono
x = cos t
y = sin t cos t
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Cartesian Equation : |
x4 = a2(x2 - y2) |
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Parametric Equation : |
x = cos t , y = sin t cos t |
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Polar Equation : |
r 2 = sec4t cos 2t |
References
J. Dennis Lawrence, A Catalog of Special Plane Curves, pp. 124-126.
2d Curves : http://www.2dcurves.com/quartic/quarticl.html
Math World : http://mathworld.wolfram.com/LemniscateofGerono.html
Jen-Chung Chuan : http://steiner.math.nthu.edu.tw/ne01/tjy/dynamic/contants/FamousCurves-e.html
Famous Curves Index : http://www-gap.dcs.st-and.ac.uk/~history/Curves/Lemniscate.html