"Then, seeing that his hosts were overthrown and his power dispersed, Morgoth quailed...but he loosed upon his foes, the last desperate asssault that he had prepared, and out of the pits of Angband there issued the winged dragons, that had not before been seen; and so sudden and ruinous was the onset of that dreadful fleet that the host of the Valar was driven back, for the coming of the dragons was with great thunder, and lightning, and a tempest of fire.
"But Earendil came, shining with white flame, and about Vingilot were gathered all the great birds of heaven and thorondor was their captain, and there was battle in the air all the day and through a dark night of doubt. Before the rising of the sun Earendil slew Ancalagon the Black, mightiest of the dragon-host,and cast him from the sky; and he fell upon the towers of Thangorodrim, and they were broken in his ruin. Then the sun rose, and the hosts of the Valar prevailed and well-nigh all the dragons were destroyed..."

Well-nigh all does not mean all, Smaug's ancestors, of course, were among the survivors. (As were Scatha the Worm's. The Withered Heath of the Grey Mountains was a breeding ground of dragons, which ended the dwarves' attempt to colonize the area. Smaug hailed from that area.)