Equation of Limaçon of Pascal

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.

Let $b$ be a real constant.

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