I need to find parametrization of following manifold. We have: $$P=\{(x,y,z):x^2+y^2=4z\}$$ and line $L=\{(x,y,z):x=2,y=0\}$.
We lookk for manifold $M=\{(x,y,z)\in P:\operatorname{dist}((x,y,z),L)\leq1\}$, where $\operatorname{dist}$ is distance between given point and $L$.
Is there some standard equation for points which fulfill above condition?