Question

\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.

Fig: 1

Fig: 2

Fig: 3