This portion involves using the program * Surfaces* to
plot some surfaces.

Please hand the answers to these questions in by the time of your lab recitation next week (i.e. Wednesday afternoon 9/11 or Thursday morning 9/12.)

Support your answers by * rough sketches* of what you see in the
computer program. The program * Surfaces* does not print very well
(and a lot of paper would be consumed ...), so please do not print
a large number of examples.

** Problem 1** Look at the graph of

for values of **c** positive, negative, and zero.

What kinds of quadric surfaces do you see for this range of **c** values?

Find the critical values of **c** when the shape of these quadric
surfaces changes.

What happens to the shape of these quadric surfaces as the absolute
value of **c** increases?

** Problem 2** Look at the graph of

for values of **c** positive, negative, and zero.

What kind of quadric surface do you see when is large?

How about when **c** is small in absolute value?

Estimate the critical values of **c** when the qualitative nature of
these quadric surfaces appears to change.

What does the graph look like for these values of **c**?

** Problem 3** Consider the graphs of

and

for the the values or .

What quadrics do you get for each of these values of **c**?

Relate what you see to the following statement:

``A cone can be a borderline case between a one and two sheeted hyperboloid.''