Let $X=A\cup B$ with $A$ and $B$ circles of radius $1$, parallels to the plane $XZ$ that lie in $(0,1,0)$ and $(0,-1,0)$ respectively.
I'm asked to characterize the $cone(X)$, the conical hull of $X$. The definition can be found here Conical Hull
I'm suggested to use polar coordinates.
I think that the solution of this problem is all the open upper semispace plus the y axis. But I don't know how to prove formally and I don't know why I am suggested to use polar coordinates. Maybe I have characterize $X$ analytically and then transform it into polar coordinates.
Answer is entire $R^3$.
Hint: Try to show that Conic hull of $X$ contains three axis X,Y and Z. Thus since Conic hull is always convex it has to contains entire space.