Change to rectangular form
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r = 4/(2+cosx)
Remember $\displaystyle r^2 = x^2+y^2$ and $\displaystyle r\cos \theta = x$.
Given, $\displaystyle r = \tfrac{4}{2+\cos \theta}$ multiply by denominator $\displaystyle r(2+\cos \theta) = 4$.
Open paranthesis, $\displaystyle 2r+r\cos \theta = 4 \implies 2r + x = 4 \implies 2r = 4-x$.
Square both sides, $\displaystyle (2r)^2 = (4-x)^2 \implies 4r^2 = (4-x)^2 \implies 4(x^2+y^2) = (4-x)^2$.
Now simplify.