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**Cartesian equation: ***y*^{4} - *x*^{4} + *ay*^{2} + *bx*^{2} = 0

Parametric Cartesian equation: x = cos*t*( (*a*^{2}sin^{2}*t* - *b*^{2}cos^{2}*t*)/(sin^{2}*t* - cos^{2}*t*) )^{1/2}, y = sin*t*( (*a*^{2}sin^{2}*t* - *b*^{2}cos^{2}*t*)/(sin^{2}*t* - cos^{2}*t*) )^{1/2}

Polar equation: *r*^{2}(sin^{2}Θ - cos^{2}Θ) = a^{2}sin^{2}Θ - b^{2}cos^{2}Θ

The Devil's Curve was studied by Cramer, a Swiss mathematician in 1750 and Lacroix in 1810. It also appears in Nouvelles Annales, a mathematics journal, in 1858.

The curve illustrated above corresponds to parameters *a*^{2} = 1 and *b*^{2} = 2.

A special case of the Devil's curve is the so-called "electric motor curve", where *y*^{2}(*y*^{2} - 96) = *x*^{2}(*x*^{2} - 100)

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