I can't understand how parametrics equations are found. For example, I realize that the parametrization of the curve given by the intersection of the plane $\ 2x+2y+z=2$ and $z=x^2+y^2$ is:
- $x=-1+\cos(t)$
- $y=-1+\sin(t)$
- $z=6-2\cos(t)-2\sin(t)$
- $0\leqslant t\leqslant2\pi$
Or that the surface of $x^2+y^2=2$ delimited by $x^2+y^2+z^2=4$ is:
- $x=\sqrt2\cos(u)$
- $y=\sqrt2\sin(u)$
- $z=v$
- $0\leqslant u\leqslant\pi/2$ and $0\leqslant v\leqslant\sqrt2$
But what is the step by step to find those equations?