Define a smooth embedded surface in $\mathbb{R}^{3}$. Sketch the surface $C$ given by

$$\left(\sqrt{2 x^{2}+2 y^{2}}-4\right)^{2}+2 z^{2}=2$$

and find a smooth parametrisation for it. Use this to calculate the Gaussian curvature of $C$ at every point.

Hence or otherwise, determine which points of the embedded surface

$$\left(\sqrt{x^{2}+2 x z+z^{2}+2 y^{2}}-4\right)^{2}+(z-x)^{2}=2$$

have Gaussian curvature zero. [Hint: consider a transformation of $\mathbb{R}^{3}$.]

[You should carefully state any result that you use.]