1. show that max{(x+y)^2 + y^2: x^2 + y^2=1} has a solution

i think i have to use continuity of f from R^2 -> R and connectedness of R and Intermediate 'Value Thm but dont know how

2. same kind of problem: show (x-1)^2 + y^2=1 has a solution on the circle x^2+y^2=1