The two paraboloids are: $S_1=\{(x,y,z)|z=2(x-1)^2+2y^2\},S_2=\{(x,y,z)|z=(x-1)^2+y^2+1\}$
Usually for me to find the surface area I try to parametrize the surface and calculate it's normal vector $\vec{n}$ to find the area by the integral $\iint_D{||\vec{n}||}$,where $D$ is the projection of the surface on the $xy$ plane.
But i can't seem to find out what $\sigma$ is here,I have found the projection of $\sigma$ on the $xy$ plane to be $D=\{(x,y,y)|(x-1)^2+y^2=1\}$ by simply substituting $z$ from $S_1$ into the $z$ of $S_2$.
I need some clarity on how to find the parameterization or the function that describes $\sigma$.