I have this question here.
The parametric curve $\vec{r}_1(t)=4t\vec{i}+(2t-2)\vec{j}+(6t^2-7)\vec{k}$ is given. Show the the curve is at the intersection between a plane and a cylinder.
If I let the plane be $x-2y=0$, then I get $4t-2(2t-2)=x-2y=2$ which is a plane so the parametric equation satisfies the equation of a plane.
What about the cylinder though? I'm very much stuck on how to set up $x^2+y^2=r^2$ to get the cylinder. Any help would be appreciated!