# What is the graph of the Cartesian equation (x^2 + y^2 - 2ax)^2 = 4a^2(x^2 + y^2)?

Jul 6, 2016

Cardioid

$r = 2 a \left(1 + \cos \left(\theta\right)\right)$

#### Explanation:

Transforming to polar coordinates using the pass equations

$x = r \cos \left(\theta\right)$
$y = r \sin \left(\theta\right)$

we obtain after some simplifications

$r = 2 a \left(1 + \cos \left(\theta\right)\right)$

which is the cardioid equation.

Attached a plot for $a = 1$