"Where do your students live?"
Translation:Где живут ваши ученики?
I suppose this is to differentiate from language students who study at school and don't need to use YouTube videos, I would feel weird saying I am a Russian student while only doing duolingo and Youtube videos. Student seems to imply a structure and a learner can be learning anything as they please, at home, in their spare time.
Ученик, the singular form of ученики, from my limited experience is used for students who follow a particular person, or discipline - 'disciple', 'apprentice', 'novice'; Whereas студенты refers almost exclusively to college students, who are engaged in exploring general knowledge.
It is not wrong, but less common. You would use this word order, for example, if you are talking about other things the students do. Like:
- Здесь ученики занимаются, а здесь обедают. = Here, the students study, and here they have lunch.
- А где ваши ученики живут? = And where do your students live?