Colin MacLaurin who was the first to study the curve (in 1742), while looking at the ancient Greek problem of the trisection of an angle: the angle formed by points ABP is three times the angle formed by AOP for points P of the trisectrix.
The area of the loop is equal to , and the distance from the origin to the point where the curve cuts the
x-axis is equal to 3.
1) With Cartesian coordinates:
y2 = x2(3+x)/(1-x).