,
which is the equation of a circle with radius
.
to one of the standard forms,
classify the surface and sketch it.
Solution: Rewriting the equation as
,
which is the equation of a circle with radius
.
Since the radius is changing and
we have a paraboloid that branches out on the positive z-axis.
Thus the graph is a paraboloid whose lowest point is (0,0,1):
by: gm