(x2 + y2)2 = 4axy2
r = 4a cosθ sin2θ
Click below to see one of the Associated curves.
|Definitions of the Associated curves||Evolute|
|Involute 1||Involute 2|
|Inverse curve wrt origin||Inverse wrt another circle|
|Pedal curve wrt origin||Pedal wrt another point|
|Negative pedal curve wrt origin||Negative pedal wrt another point|
|Caustic wrt horizontal rays||Caustic curve wrt another point|
(x2+y2)(y2+x(x+b)) = 4axy2
or, in polar coordinates
r = -b cosθ + 4a cosθ sin2θ.
The word folium means leaf-shaped.
There are three special forms of the folium, the simple folium, the double folium and the trifolium. These correspond to the cases
b = 4a, b = 0, b = a
respectively in the formula for the general form.
The graph plotted above is the double folium. There are separate entries for the simple folium and the trifolium.
The double folium is the pedal curve of the tricuspoid where the pedal point is mid-point of one of the three curved sides.
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