Parametric equations of the curves

Question

Try to sketch by hand the curve of intersection of the parabolic cylinder y = x ^ 2 and the top half of the ellipsoid x ^ 2 + 9y ^ 2 + 9z ^ 2 = 81 Then find parametric equations for this curve.

(x(t), y(t), z(t))=

Answer 1

x ( t ) = t

y ( t ) = t²

z ( t ) = [ 81 - t ² -9 t⁴ ]/ 9