Why is the set of points in $\mathbb{C}P^2$ where a non-degenerated quadratic form vanishes biholomorphic to $\mathbb{C}P^1$?

Question

Let $Q: \mathbb{C}^3 \rightarrow \mathbb{C}$ a non-degenerated quadratic form and let $S=\{[z_1,z_2,z_3] \in \mathbb{C}P^2 : Q(z_1, z_2, z_3) \}$. My lecture notes on Riemann surfaces mention that $S$ is then a complex sub-manifold of $\mathbb{C}P^2$ of dimension $1$, biholomorphic to $\mathbb{C}P^1$. Why is that the case? I don’t know a lot about quadratic forms and the projective space (apart from the definitions and some basics) and couldn’t find a proof.