Could you provide the model # of your machine.

Or you could Google, the model# of the Fax HPXXXX and the word answering machine for starters.

Does this help

Here is a link that might be useful: Fax and answering machine

to have a different ring you have to get that from the phone company, I have what is called distinctive ring it has a different number but it is NOT a separate line, same line only one line but with a separate number which will cause the phone to ring a specific way, mine is 2 rings in a row ring ring and when my fax hears that ring it knows to pick that call up, my regular phone ring is not picked up by the fax. There are settings in the fax itself to set for a distinctive ring situation. Mine is also an HP just go through the book it will tell you exactly what to do.
But if you leave it on your regular line plugged in then it will try to answer any call. You would need to check on your specific answer machine book for how your's works with a fax machine.