Let $p = (0,0)$, $q = (0,1)$, $r = (\imath, 0)$ be points of $\mathbb{C}^2$. What is the dimension of the $\mathbb{C}$-vector space
$$\{ f(X,Y) \in \mathbb{C}[X,Y] \mid \deg f \leq 2 \text{ and } f(p) = f(q) = f(r) = 0 \}$$
where by $\deg f$, we mean the total degree of the polynomial $f$?