What is the resulting figure called when describing the equation yz=4 in R^3?

[navalava]

Homework Statement

Describe and sketch the surface in R^3:
yz=4

Homework Equations

The Attempt at a Solution

So y= 4/z and z=4/y, and in 3-d that becomes two hyperboloids of one sheet...how do i connect them and what is the resulting figure called? I really appreciate the help!

 

[dynamicsolo]

You are correct in that you get two pieces, but they are not hyperboloids (those types of surfaces require two of the perpendicular cross-sections to be hyperbolas). Since this has the same cross-section for all values of x , the best name for it might be a "hyperbolic cylinder". (And the two parts won't be connected.)