\text { Consider a surface } \mathrm{S} 1: \mathrm{z}=x^{2}+\frac{y^{2}}{2} \text { and a plane } \mathrm{S} 2: \mathrm{x}=0 (1) Find the parametric representation of the curve of intersection of S1

and S2. (2) Find the center of the osculating circle to the curve of the intersection at any point.