Find all points on the curve $y+x=x^2+y^2$ where the tangent line is horizontal.

Select one:

a$.(0,0)$

b$.(\frac{1}{2},\frac{1+\sqrt[\phantom{2}]{2}}{2})$ and $(\frac{1}{2},\frac{1-\sqrt[\phantom{2}]{2}}{2})$

c$.(\frac{1}{2},\frac{-1+\sqrt[\phantom{2}]{2}}{2})$ and $(\frac{1}{2},\frac{-1-\sqrt[\phantom{2}]{2}}{2})$

d$.$ None of the above