Eucalyptis trees are not inherently dangerous to houses. It depends on how big it is and how close it is to the house......

If you have one, keep it trimmed short. (When I bought my house, it included 6000 sq meters of woods, and I could not get to the back because of eucalyptus trees that had been blown over by storms.) If you are thinking of planting one, I would advise against it because they suck up all the water around them, destroying everything else. The wood has a high water content and takes twice as long a s other wood to dry out so it can be used in a fireplace.

Depends how near - if its over 40 feet away, and its a full sized Eucalyptus gunii (50 feet high) then that's far enough away. Any closer and I'd be worried about my house foundations.

If it IS too near, why not try coppicing it?