I think you can just use common sense here.

The 9 does NOT affect the min and the max.

I now see that and ,

so the min is 9 which occurs along the x axis and the y axis.

Next insert the constraint in the function to get the max along the circle in the first quadrant.

.

Now maximize this wrt x and you get x=1, since we're only in the first quadrant.

That gives and a max of 11.

I also got this via LaGrange, to check my work.