Origins of Smaug

[AndMorgothCame.]

Smaug, the last of the Uruloki, is the only Dragon around during the Third Age (that we know of), but I have never read or come across information on his beginnings. Was he the offspring of earlier dragons? I've never heard of dragon reproduction, and I believe all were created by Melkor. . .
Other than the theory of him being the last of the Fire Drakes of the North who flew into Erebor and settled, is there any other writing, rumor, or word about where he came from, and if he ever knew Melkor as a master?

And what luck that Smaug and the Balrog of Moria should be slain before the war of the Third Age. Those two may have assured a win for Sauron.