Let $k$ be a field with at least 4 elements, and let $C: XZ = Y^2$ be a subset of $\mathbb{P}_k^2$.
I'm trying to prove that if $Q(X,Y,Z)$ is a quadratic form which vanishes on $C$, then $Q = \lambda(XZ-Y^2)$.
Let $k$ be a field with at least 4 elements, and let $C: XZ = Y^2$ be a subset of $\mathbb{P}_k^2$.
I'm trying to prove that if $Q(X,Y,Z)$ is a quadratic form which vanishes on $C$, then $Q = \lambda(XZ-Y^2)$.