  Let $K$ be a locally compact non-discrete field of characteristic $p>2$ and
$Q$ be a non-degenerate isotropic binary quadratic form with coefficients in
$K$. We obtain asymptotic estimates for the number of solutions in the two-fold
product of a discrete subring inside $K$, of the inequalities of the form
$|Q(x,y)|<\delta$ for some $\delta>0$, where $| \cdot |$ is an ultrametric
absolute value on $K$. The estimates are obtained in terms of continued
fraction expansions of the coefficients of the quadratic form $Q$.
