Ron, I read the 4 posts below and I don't think this is life threatening after 20 years and within a couple feet of the end(don't park a baby bed underneath it). While it is not recommended to put the hole there, sometimes "tradeoffs" are made during construction and remodel, etc to avoid coming under the joist. Watch for a crack under the hole.
You could always fix it by taking it out, run the duct underneath, and then nail another board along side for support. I'd probably only do that if there was a loadbearing wall above and on top of the joist.
I like the strap idea. You could also get some short 2by10s and bridge over to the adjoining joists on the long span side of the joist hole(and maybe even strap them). This may add a little bit more support. You could also put in a support post from the floor but I assume the hole was cut to start with to avoid something hanging into the finished basement unless it was done to cover up a mistake by the guy putting in the duct work. Good luck.