Imagine the xy-plane as being the ground, and the z-axis represents height. So, z=0 is "ground" level, z=1 is one unit above the ground, z=2 is two units up, etcetera. What we are doing is taking horizontal cross-sections of the 3D graph.
First, rewrite the function as
So each slice of the graph is a vertical ellipse with axes z/2 tall and z/3 wide.
The only point (x,y) satisfying this is the origin, (0,0)
See if you can visualize it from here.