1. The problem statement, all variables and given/known data Solve for the vector function that represents the curve of intersection in the following two surface: z = sqrt(x^2 + y^2) and z = 1 + y 2. Relevant equations 3. The attempt at a solution Through blind trial and error, I managed to get the book-specified answer of x = t, y = 0.5(t^2-1) and z = 0.5(t^2+1). What I'm curious about is why using parametric equations wouldn't work in this case. Which leads to what kind of right I have to using seemingly random functions when parameterizing a vector function. I first worked with x = cos(t) and y = sin(t) to get z = 1, only to get something like 1 = 1 + sin(t), which got me stuck. Only after making some wild assumption x = t did I get the exact same book answer.