we find that the surface is a hyperboloid of one sheet.
to one of the standard forms, classify the surface and sketch it.
Solution: Rewriting the equation as
we find that the surface is a hyperboloid of one sheet.
To sketch it analyze the traces. There are hyperbolas in both the
xz and yz planes. For a fixed z the equation can be put in the form
,
which is the equation of an ellipse..
The surface has the following representation.
by: gm