[Grammar] Was/were/have/has/had/did/do/does

Question:

Student A: Where ( have you lived / are you living / did you live ) now that you have left home?
Student B: In a small house in South Manchester.

I am asking for answer and the explanation. My answer is "are you living" but I think "did you live" is also correct. Both of the answer seen means the same. Does any difference between are and did? If yes, when we should use is and are or do and does? Thanks in advances.

"Now that you have left home" indicates that you are asking about the present. So "are you living."

"Did you live" is about the past, a completed past action. If I ask "where did you live?" it is not asking about where you are now, but where you lived in the past.

Thanks.