Find a parametric equation of the given curve.

Question

The intersection of the paraboloid $z=x^2+y^2$ and the parabolic cylinder $y=x^2$ in $\mathbb{R}^3$

Answer 1

$z=x^2+y^2$ Substitute $y=x^2$

$z=x^2 + x^4$

$\begin{cases}z=t^4 + t^2\\y=t^2 \\x=t\end{cases}$