Some QCH Kähler surfaces with zero scalar curvature

We prove that some well-known Kähler surfaces with zero scalar curvature are QCH Kähler. We prove that the family of generalized Taub-NUT Kähler surfaces parameterized 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 Burns metric is of Calabi type.