Step 1: Identify the reporting verb.
The reporting verb is "said to," which should be changed to "told" in indirect speech for correctness.
Step 2: Change the pronouns.
In direct speech, "your" refers to me (the listener). Therefore, "your" changes to "my" in indirect speech.
Step 3: Check the tense of the reported speech.
The reported speech is in the present tense ("is to take care"), and since the reporting verb is in the past, the tense remains the same because it is a universal truth/duty.
Final Answer:
The teacher told me that my duty is to take care of my parents.