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## Homework Statement

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

## Homework Equations

## 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.