So I am given the function $x^2 + y^2$ and the constraint $x^2 -2x +y^2 -4y=0$. Must find max and min values (answers are $f(0,0)$ is a min and $f(2,4)$ is a max.) I use $\nabla f = \lambda \nabla g$. and get $x= \lambda(x-1)$ and $y=\lambda(y-2)$. Not sure if I messed up there or what, but I haven't been able to get to the answers once I plug $x$ and $y$ into the constraint. Any help at all is appreciated.