Space Curve Intersecting a Parabloid

[k_squared]

Homework Statement

At what point does the curve $\vec{r}(t) = <t,0,2t-t^2>$ intersects the paraboloid $z=x^2+y^2$

Homework Equations

None Known

The Attempt at a Solution

I assume that it might be easier to parametrize $z=x^2+y^2$, but I'm not sure how to do that or if there's a more standard approach.

I missed a day of class and I can't find any examples more than vaguely similar to this in the book. :\


Thanks for any help!

 

[Karnage1993]

You can also try to de-parameterize $\vec r(t)$. Hint: there won't be any y terms.