I'm trying to find the parametrization of the intersection of a sphere and a plane:
\begin{cases} x^2+y^2+z^2=1 \\ x+z=0 \end{cases}
And I end up getting $2x^2+y^2=1$, but I cant't think of a way to write that in the form of $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, so I can then parametrize the equation.
We have $$2x^2+y^2=1$$ $$\frac{x^2}{\frac{1}{2}}+y^2=1$$ $$\frac{x^2}{(\sqrt{\frac{1}{2}})^2}+\frac{y^2}{1^2}=1$$