The Sphinx was borne from the union of the no account snake torso-ed Goddess, Echidna, and the deadbeat father of all monsters Typhon. Due to the eclectic genetics of her parents her lovely human face was perched atop the body of a winged and ample bosomed lion, with a decorative snake tail on the back end. Note that she did not have a snakes tail, her tail was an entire Snake, attached to her lion butt.
The Sphinx’s early life is murky, but at some point she flew from her homeland of Ethiopia to take up residence on the coast near Athens, on a big rock by the road. Shunned by cliquish lions and smug people bodied humans the Sphinx grew embittered with the politics of her new home. Hungry and alone the Sphinx decided to channel the pain of her isolation into a cruel game of riddles that she would spring on passers by. The prize: go about your day. The punishment: Strangulation and then consumption. The historical records are unclear if she strangled them with her lions paws and ate them with her human mouth, or if she constricted the snake around their throats so it could then swallow them upwards into the Lion Butt. I imagine this being a source of contention for both ends.
She ran this grift for an unspecified period of time until Oedipus sauntered by and solved her riddle. Yes, that Oedipus. The Sphinx took it poorly and committed suicide by hurling herself off of the side off of the rock. Oedipus went on to have a terrible day. The end.