Only #1 is correct.
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Persian LearnerDoes the above sentence mean that she explained something to the teacher?No. "Answer to" has a different meaning. Take a look at the explanation and the example sentences of "answer" as a verb (#3) in the link below.
Persian LearnerAre both of the above sentences correct?No. 'answer to' is used differently. When you 'answer to (someone)', they are in a position of authority over you and you have to explain to them what you have done.