Find a parametrization of the intersection curve between two surfaces in $\mathbb{R^3}$ $x^2+y^2+z^2=1$ and $x^2+y^2=x$. Find a parametrization of the intersection curve between two surfaces in $\mathbb{R}^3$
$$x^2+y^2+z^2=1$$ and $$x^2+y^2=x.$$
I know that $x^2+y^2+z^2=1$ is a sphere and that $x^2+y^2=x$ is a circular cylinder. Any help is greatly appreciated, thank you. 

+1) The polar equation of $x^2+y^2=x$ is $r=cos\theta$ and so we have $x=rcos\theta$ and $y=rsin\theta$ as parametrics (with $r$ known) Substituting into the first equation, you can solve for $z$. Note that $1-cos^2\theta=sin^2\theta$ Hope this helps, if not or incorrect, I will take it off.
