  In this paper we prove that some well known K\"ahler surfaces with zero
scalar curvature are QCH K\"ahler. We prove that family of generalized Taub-Nut
K\"ahler surfaces parametrized by $k\in[-1,1]$ is of orthotoric type for
$k\in(-1,1)$ and of Calabi type for $k\in\{-1,1\}$.
