Equation of Limaçon of Pascal
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Theorem
Let $C$ be a circle of diameter $a$ whose circumference passes through the origin $O$ and whose diameter through $O$ lies on the horizontal.
Polar Form
The limaçon of Pascal can be defined by the polar equation:
- $r = b + a \cos \theta$
Cartesian Form
The limaçon of Pascal can be defined by the Cartesian equation:
- $\paren {x^2 + y^2 - a x}^2 = b^2 \paren {x^2 + y^2}$
Sources
- Weisstein, Eric W. "Limaçon." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Limacon.html