The Stacks project

Exercise 111.61.3. Let $k$ be an algebraically closed field. Let $X \subset \mathbf{P}^3_ k$ be a smooth curve of degree $d$ and genus $\geq 2$. Assume $X$ is not contained in a plane and that there is a line $\ell$ in $\mathbf{P}^3_ k$ meeting $X$ in $d - 2$ points. Show that $X$ is hyperelliptic.