Find parametrisation of a surface's boundary

Let S be a surface such that x^2 + y^2 + 4z^2 = 1 (S is in R^3)
Let U be the finite region of S satisfying z > 0 and let C be the boundary of U.

Then: find a parametrisation of C.

I know the answer but not sure how/why. What is meant by 'boundary' exactly? I thought it would be the 'shell' or effectively the surface area of the dome-shaped surface

Thanks,

The boundary ('edge' of the surface) occurs when z = 0:
x^2 + y^2 = 1 with z = 0; this is a unit circle.

So, one answer is c(t) = (cos t, sin t, 0) with t in [0, 2π].

I hope this helps!