Question

How do you determine if `f(x,y)=(x^2y^2)/sqrt(x^2+y^2)` is homogeneous and what would it's degree be?

Answer 1

`f(x,y)` is homogeneous of degree 3

Explanation:

Let's evaluate:

`f(alphax,alphay) = ((alphax)^2(alphay)^2)/sqrt((alphax)^2+(alphay)^2)=(alpha^4x^2y^2)/sqrt(alpha^2(x^2+y^2))=(alpha^4x^2y^2)/(alphasqrt(x^2+y^2))=alpha^3f(x,y)`

so we can see that `f(x,y)` is homogeneous of degree 3