back up disk drive

Can you use a backup diskdrive to back up two different computers? I have a macbook and a imac

The answer is yes.
You can partition your HD in 2 or run it without partitioning it, your choice.
Just plug the external HDD into the macbook and run a Time Machine backup as normal
The Time Machine system is clever enough to realise you are backing up a different computer and will create a brand new backup file. Each backup file is created with the name of the machine you are backing up, so for example if you look on your external HDD you will see a backup file called something like "Jacks_iMac4835824.sparsebundle". So the macbook would automatically create a new backup file called "Jacks_Macbook54478457.sparsebundle" etc

No need to worry about partitioning and no need to worry about it getting confused with backing-up/restoring multiple machines on the same HDD.

BUT
While everything will work as intended if you chose not to partition the disk, it is a good idea and will save you from the situation where if the disk is almost always plugged into the iMac, the iMac will have more backups than the MacBook and thus leave very little space for the MacBook. Going on from that, what I would do is create two partitions and share the second partition over the network to the MacBook. You would do the initial backup of the MacBook while connected through gigabit ethernet, and then subsequent backups over wireless.