  It is well-known that the Hasse principle holds for quadric hypersurfaces.
The Hasse principle fails for integral points on smooth quadric hypersurfaces
of dimension 2 but the failure can be completely explained by the Brauer-Manin
obstruction. We investigate how often the family of quadric hypersurfaces $ax^2
+ by^2 +cz^2 = n$ has a Brauer-Manin obstruction. We improve previous bounds of
Mitankin.
