This is exactly the question Phaeton asked his mother, Clymene. When his mother told him that his father was the sun god, Helios, he wanted proof. This was a reasonable request, in view of the fact that Merops was the earthly husband of Clymene. We read of this story in book 2 of Ovid's Metamorphoses.
At last Phaeton got to go and see his father, and his father even allowed him to drive the sun chariot. This was to be the ultimate downfall of Phaeton. As he was riding the sun chariot, he got too close to the earth, as he could not control the horses of the chariot. For this reason he was about to burn the earth and destroy human civilization. For this reason, Jupiter killed him with a thunderbolt to contain the damage.