retain FV encryption key from before on fresh install?

I currently am running 10.9.3 with File Vault on. I do weekly backups to an external drive.

10.9.3 is a result of updates several several generations deep- i.e. all the way back to Lion. I would like to wipe the drive and do a fresh install- however the external drive is encrypted as well. I am curious abut how, using File Vault, this is handled, whether one has an opportunity to enter the old key for use on the new install- and whether or not one still has access to the encrypted backup disk after the new install? Does File Vault de facto generate a new encryption key on a new install or can one use the old key?

I did a search for this here and came up empty handed. Thanks.

Expat42451

FreakinEurekan

Thanks for the information. I was under the impression that when File Vault was enabled, that the back up drive was also encrypted with the same key.

That is definitely good to know. Also good to know that a nuke, pave, reinstall and restore shouldn't be a problem.

Many thanks

Expat