LaGrange multiplier question

I have a function of f (x,y) = x^2 + 2y^2 which has a constraint of x^2 + y^2 is less than or equal to 4

My LaGrange function is: x^2 + 2y^2 - lambda(x^2 + y^2 - 4)

dL/dx 2x - lambda 2x = 0

dL/dy 4y - lambda 2y = 0

dL/lambda x^2 + y^2 - 4 less than or = 0

So, (0,0) is one possible critical point as is (0,2) and (0, -2) and I used these and got a maximum of f(x,y) = 8 for (0,2) and (0, -2) and min f(x,y) = 0 at (0,0) but....

why can we not use (2, 0) and ( -2,0)????? Can someone please explain why?????

Thanks for your efforts, Frostking