I've been messing around a bit with a 4d algebra, and I keep coming across a shape described by this formula:

(w-x)^2 + (y-z)^2 = c

What is it, and what is it like? When c = 0, it's a 2d plane (unless I'm mistaken), but what happens for other c? The 3d equivalent would be an infinite cylinder, but when I try to picture this in 4d I keep getting two intersecting cylinders, which I know isn't right.