1. The problem statement, all variables and given/known data Going over some old tests, I am asked to find the contour of the function: T = 100 - x^2 - y^2 at T = 100, T = 0, etc. I have a question regarding the contour at T = 100 2. Relevant equations 3. The attempt at a solution Consider T = 100 100 = 100 - x^2 - y^2 0 = -x^2 - y^2 This is a circle with radius 0. I knew at the time that this must be the top of the paraboloid. However, I also noted that 0 = -x^2 -y^2 0 = x^2 + y^2 y^2 = -x^2 y = sqrt(-x^2) Is it correct to determine this result as "there exists a real solution only at x = 0, thus the only point at this contour is (0,0)"?