Circles in different Dimensions in the $X-Y-Z$ Plane.

Question

Explain the difference in the graphs of $(x – 1)^2 + (y + 3)^2 = 4$ and $(x – 1)^2 + (z + 3)^2 = 4$, both in the $(x,y,z)$-space.

Answer 1

$(x-1)^2+(y+3)^2=4$ is a hollow cylinder passing through the x-y plane.

$(x-1)^2+(z+3)^2=4$ is a hollow cylinder passing through the x-z plane.

This graph will express it better,