1. The problem statement, all variables and given/known data Find a function of two variables whose level curves are parabolas with vertex (0,0) with a hole in the parabolas at the origin. 2. Relevant equations No special equations come to mind. 4ay=x2 may be a little useful. 3. The attempt at a solution The first thing I thought of was y=x3/x, but that doesn't include the third variable. I know the parabolas can have any value for a or face any direction, but I do not know how to include z so that the function will remain having level curves as stated. Are there any other functions with these properties? Any input will be appreciated.