If the curve of intersection of the parabolic cylinder

Question

y = x^2
and the top half of the ellipsoid
x^2 + 5y^2 + 5z^2 = 25.
Then find parametric equations for this curve.

Answer 1

the cylinder has parametric equations
x = t
y = t^2
Intersect that with the ellipsoid and you get

x = t
y = t^2
z = 1/5 √(25-t^2-5t^4)

Answer 2

I got sqrt 5 on the bottom

Answer 3

and you would be correct.
I knew there was something not right.