I think it would depend on how formal your teacher wants you to be. The format is quite common, but I'm not sure of the formally correct way to set off the starting question.
There are three sentences:
"What is your favorite sport?" OR "What are your favorite sports?"Imagine being asked this question[ ! ] . Yes, this is an imperative sentence, and the [understood] subject is "you." I don't see how this adversely effects your choices in framing the next question:
What would you choose? OR What would your answer be? Either option requires "would," because of the word "imagine." I think both options are equally correct. I believe in the first option the subject is "answer," and in the second option the subject is "you," as you suggest. I see no problem with either solution.
I'd urge you not to attempt to combine the second and third sentences.
- A.
Edit. Sorry, I'm not awake yet. I never noticed the present participle. I see no problem with that construction, followed by either option.
Being in a hurry, what would you choose? Being in a hurry, what would your choice be? Thinking ahead, what would you do?
Imagining being asked that question, what would your answer be?
Okay, now I see it. You're absolutely right, Helen. Only the other option is correct, for the reason you originally suggested.
The question is not capable of imagining.
As a participial phrase functioning as an adjective, "Imagining being asked that question" can only modify "you." (for contextual reasons)
Imagining being asked that question, what would you choose? I'll say it's correct - but rather ugly!