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