Strophoid Base curve
A strophoid, also known as a logocyclic curve or a foliate, is a cubic curve generated by increasing or diminishing the radius vector of a variable point Q on a straight line AB by the distance QC of the point from the foot of the perpendicular drawn from the origin to the fixed line.
The polar equation is
- <math>r=a\ \cos2\theta/\cos\theta</math>.
The Cartesian equation is
- <math>y^2 = x^2(a-x)/(a+x)</math>,
where a is the distance of the line from the origin. The curve resembles the Folium of Descartes, and has a node between x = 0, x = a, and two branches asymptotic to the line x = −a.
The curve has two more asymptotes, in the plane with complex coordinates, given by
- <math>x\pm iy = -a</math>.
A curve: <math>r=a\ \sin(\alpha-2\theta) / \sin(\alpha-\theta)</math>
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