for some reason, I can't do the math. I have worked out that $(x^2+y^2-1)^2+4y^2=r^2((x+1)^2 + y^2)^2$ should be the circle $$\left(x-\dfrac {1+r^2}{1-r^2}\right)^2 + y^2= \left(\dfrac{2r}{1-r^2}\right)^2,$$ using some prior knowledge, however I can't prove it. Can someone help me on my way? Many thanks in advance.