Define a second elliptical cylinder such that the curve r is the cross section of both cylinders.

Question

Hello could somebody help me to solve this problem, I'm really struggling.

let $\textbf{r}(t)=\dfrac{\sin(t)}{\sqrt2}\textbf{i}+\cos(t)\textbf{j}+\dfrac{\sin(t)}{\sqrt{2}}\textbf{k}$

$\text{with }0 \leq t \leq 2\pi\text{ and }2x^2+y^2=1$

Define a second elliptical cylinder such that the curve r is the cross section of both cylinders.

So I know how to get from two planes to a curve that represents the intersection, but somehow I can't figure out how to do this problem.

If someone knows the answer and would like to share it, it would be very much appreciated:)

Thank you very much.