in the planes x = k, y = k, z = k. Then identify and
sketch it.
This says that if y is held fixed then (x,z) satisfy
the equation of a circle centered at the origin of radius sqrt(1+y^2). The 5 circles corresponding
to y = -2, -1, 0, 1, and 2 (the y traces for y = -2, -1, 0, 1,2) look like this:
To continue, if we set x = 0 the resulting equation is
which is the equation of a hyperbola:
Finally, if we set z = 0 the original equation reduces to
which is another hyperbola:
When these traces are assembled in one graphic one gets this surface:
