$$\left(x^{2}-2\right)^{2}+\left(y^{2}-2\right)^{2}=2$$
Pretty much as per the title. Was set as a graph sketching exercise. Can see that it will have symmetry around all 4 axes but unclear as to how I would go about sketching this. I guess I could look at key points e.g. $(1,1), (\sqrt{3},1)$ but not sure it's a great method. Any help appreciated
First, graph $\left(x-2\right)^{2}+\left(y-2\right)^{2}=2$.
Then graph $\left(x-2\right)^{2}+\left(y^{2}-2\right)^{2}=2$.
Then graph $\left(x^{2}-2\right)^{2}+\left(y^{2}-2\right)^{2}=2$.
(At each step explain how the graph is transformed.)