Cartesian equation: y
(a+x) = x(3a-x)
Polar equation: r = 2a sin(3
)/sin(2)
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
The trisectrix of Maclaurin is an anallagmatic curve.
Another form of the equation is r = a sec(/3) where the origin is inside the loop and the crossing point is on the negative x-axis.
The tangents to the curve at the origin make angles of 
60
with the x-axis.
The area of the loop is 3
3a and the distance from the origin to the point where the curve cuts the x-axis is 3a.
It is the pedal curve of the parabola where the pedal-point is taken as the reflection of the focus in the directrix.
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