For which real numbers \(a>0\) and \(b>0\) does the limit

\[ \lim_{(x,y)\to(0{,}0)}\frac{|x|^a|y|^b}{x^2+y^2} \] exist, and what is it equal to?

The limit does not exist when \(a+b\le 2\), otherwise, it is equal to \(0\).