Folium of Descartes

 

Cartesian Equation : 

x3 + y3 = 3xy

Parametric Equation : 

x = at/(1 + t3)   ,   y = at2/(1 + t3)

Polar Equation : 

1/r = cot t cos t + sin t tan t

 This folium was first discussed by Descartes in 1638 but, although he found the correct shape of the

 curve in the positive quadrant, he believed that this leaf shape was repeated in each quadrant like the

 four petals of a flower.

Tangent

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