y2(a + x) = x2(3a - x)
r = 2a sin(3θ)/sin(2θ)
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(θ/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√3a2 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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