course

You have the right idea. If c = 4, then the equation is 16 - x^2 - y^2 = 4. Rearranging this gives you x^2 + y^2 = 12, which is a circle centered at the origin with radius sqrt(12).

More generally 16 - x^2 - y^2 = c rearranges to x^2 + y^2 = 16 - c, which is a circle centered at the origin having radius sqrt(16-c).

For c > 16 the square root has a negative argument, and therefore doesn't exist. So the graph of this function does not extend higher than z = 16.

If you consider how the z = 0, 4, 8, 12 and 16 slices stack you get a good picture of the shape of the graph (you get circles whose radii decrease at an increasing rate). If you also consider the x-z and y-z slices you see that the graph is parabolic in those planes, so the surface is a paraboloid of revolution about the z axis.

I believe these ideas are covered pretty well in the assigned problems on the relevant sections (in this case section 7.2, give or take 1 section depending on the version of the text you're using).

I'll be glad to answer additional questions.

Dave,

Sorry to bother you again, but I seem to be struggling to

find examples of the types of problems I'm finding on the

test.

The one I'm working with now asks me to ""identify"" the

contour map of f(x,y)=16-x^2-y^2, C=4,8,12

What does ""identify"" mean in this context?

From reading section 7.3 I think I understand that ""C"" is

the Z coordinate (or elevation for instance)

Am I to draw the map?

I need help on how to approach this. I could find no

examples in the book or on the CD's.

Thanks.