Answer
(a) See the graph.
(b) $(x^2+y^2)^2=4x(x^2-y^2)$
Work Step by Step
(b)
$x=r~cos~θ$
$y=r~sin~θ$
$r^2=x^2+y^2$
$r=4~cos~3θ$
$r=4(cos~2θ~cos~θ-sin~2θ~sin~θ)$
$r=4(cos^3θ-sin^2θ~cos~θ-2sin^2θ~cos~θ)$
$r=4(cos^3θ-sin^2θ~cos~θ)$
$r=4(\frac{x^3}{r^3}-\frac{xy^2}{r^3})$
$r^4=4x(x^2-y^2)$
$(x^2+y^2)^2=4x(x^2-y^2)$
