How to define a function with three cases?

Let f(x,y)=0 for (x,y)=(0,0) and f(x,y)=x^2/(x^2+y^2) for x^2>y^2 and f(x,y)=y^2/(x^2+y^2) for x^2<y^2. How to do this.

Please avoid multiple posting. I answered the first here

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