(x2 + y2)(y2 + x(x + a)) = 4axy2
r = a cosθ (4sin2θ - 1)
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 trifolium. There are separate entries for the simple folium and the double folium.
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