Sketch the Level Curve z = k?

Josh

New member
I know for this kind of problem I should set the equation equal to the values of k but I don't know how to interpret that Information. To that end here is a screen shot of the problem.

http://i218.photobucket.com/albums/cc73/Sarge525/curves.jpg

I am mainly trying to understand what causes the circle to bow out in some instances and then also what causes it to have a dot in the center.
 
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