[SOLVED] shortest distance 1. The problem statement, all variables and given/known data Find the shortest distance to the origin given the quadric surface x^2 + y^2 - 2zx = 4 2. Relevant equations 3. The attempt at a solution F = x^2 + y^2 + z^2 g = x^2 + y^2 - 2zx = 4 Well I initially substituted y^2 = 4 + 2zx - x^2 into F F = 4 + 2zx + z^2 which leads to z = 0 x = 0 and so y = 2, however this is not the shortest distance. I know this is because of the boundaries of the surface; however I don't know in what way to modify my analysis so that I can take into account the boundaries and get the shortest distance.