A limit with parameters

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 $$0$$.