[Math] What does the level curve xy = 3 to the graph xy = z look like

Question

I got this example from MIT courseware class on multivariable calculus it was an example during the lecture. Just having difficulty with the visual.

Looking for the level curve xy = 3 to the graph xy= z.

Answer 1

Here is a plot of $z = x y$ (blue) and $z = 3$ (orange):

Your question is a bit awkward. The plot of $x y = 3$ is really a hyperbola that lies in the two-dimensional $xy$ plane. The plot of $z = x y$ is a three-dimensional surface in a three-dimensional $xyz$ space.