Find a parametrization of the intersection curve between surfaces

Question

Find a parametrization of the intersection curve between the surfaces $−3x^2+2z=10$ and $4x^2+10y^2=5$. You should parametrize such that $y=k\sin(t)$ for some constant k.

The answer should be in vector form.

I'm a bit unsure about how to attack this question. Some step by step help would be nice but some hints or answer is okay too.

Answer 1

The first surface is a parabolic cylinder, while the second is an elliptic cylinder. A parameterisation of the second one is $x(u,t)=\frac{2}{\sqrt{5}}\cos t, y(u,t)=\sqrt{2}\sin t, z(u,t)=u$. Now replace these values in the first one.

Answer 2

Hint: The second equation is an ellipse which might be parametrized as $\bigl(\sqrt{2.5}\cos(t),\sqrt{0.5}\sin(t)\bigr)$.