For any $A(z),B(z),C(z) \in \mathbb{C}[z]$, we study the zero distribution of a table of polynomials $( P_{m,n}(z) ), m,n \in \mathbb{N}$ satisfying the recurrence relation $P_{m,n}(z)=A(z)P_{m-1,n}(z)+B(z)P_{m,n-1}(z)+C(z)P_{m-1,n-1}(z)$ with the initial condition $P_{0,0}(z)=1$ and $P_{-m,-n}(z)=0$ $\forall m,n \in \mathbb{N}$. We show that the zeros of $P_m,n(z)$ lie on a curve whose equation is given explicitly in terms of $A(z)$,$B(z)$, and $C(z)$. We also study the zero distribution of a case with a general initial condition.