As part of a longer proof, I have encountered the statement:
If $C$ is an irreducible projective curve of degree $4$ and $p_1, \ldots p_5 \in C$, then there is a conic that passes through them.
I see that the $5$ points can't be collinear as this would contradict Bezouts Theorem. Also, if $L_1$ is the unique line through $p_1$ and $p_2$ and $L_2$ is the unique line through $p_3$ and $p_4$ then $L_1 \cup L_2$ is a conic passing through $4$ them, but not necessarily through $p_5$