Answer:
Step-by-step explanation:
1. Oedipus as the King of Thebes is so determined to find out the truth of his identity because he wanted to be sure that he didn't fulfill the prophecy he heard when he was a young boy.
The prophecy was through the oracle that he was fated to kill his father and marry his mother.
And describing Liaus by Jocasta, Oedipus was worried whether Liaus was his real father or not, and if he is, Jocasta must have been his father. But he wanted to be sure.
2. Jocasta was unwilling to help because she was suspecting Oedipus could be her son, and she doesn't want to find the truth.