Consider the cone formed by the revolution of $x=1$ and $y=1$ about $y=x$ for positive values. The vertex is at $(1,1)$ (in 2-space). Then slice the cone with a plane to generate a conic section.
What are the equations for the conics?
I'm not sure because the lower half of this cone is now bounded in $(0,1).$ Slicing with the right plane should yield say a hyperbola like figure but with the two branches being small and large. The small branch is bounded in $(0,1).$
Thanks.