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

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Answer 1 · 2016-07-06T16:50:46

Cardioid

$r = 2 a(1+cos(theta))$

Transforming to polar coordinates using the pass equations

$x = r cos(theta)$
$y = r sin(theta)$

we obtain after some simplifications

$r = 2 a(1+cos(theta))$

which is the cardioid equation.

Attached a plot for $a = 1$

enter image source here

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