Some QCH Kahler surfaces with zero scalar curvature

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