I think they all sound a bit stilted to be honest. When asked about their hobbies, I think most native speakers wouldn't use 'hobby' in a reply. Answers might include 'I'm in a band, 'I play the piano', 'Hiking', 'I play a lot of sport', etc.
I think people would usually ask "Do you have any hobbies?" which leaves it open-ended. Asking "What's your hobby?" makes it squirmy/uncomfortable, like you're assuming/presuming that people only have one.
The answer may just be one thing, but it's polite to leave it open. "Do you have any hobbies" could be answered by "I like to swim," or "I like swimming," or "I swim a little," or just "swimming."
When asked "Do you have any hobbies?" most would not include 'hobbies' in the answer.
As JohnnyG says above (and I suspect Lothor's comment is not completely unrelated) the question itself sounds like it was translated directly from Japanese あなたの趣味はなんですか？
The question is completely typical in Japanese, but in English it sounds slightly stilted because of the use of the singular "hobby" (as if the person being asked is assumed to have only one hobby). For beginning English learners, its a very slight transgression, and completely forgivable. I wouldn't even call it a mistake. But for people who aspire to move beyond "beginner" status, they should be aware of the slight awkwardness of the phrase.
I agree. It seems similar to me to 遊ぶ which was translated to 'play' in my studies.
The first time I heard 遊ぶ applied to adults it threw me for a loop because in English the word 'play' is usually reserved for describing children's actions and only rarely and in specific circumstances used for adults.
I agree (b) for both. I think (a) is acceptable but not so common. As the others said, the whole phrase sounds like a classroom exercise, not something you often say in real life. It's kind of like これはペンです -- how often do you say this in real life?
Even if somebody asks me directly "Do you have any hobbies?" then I wouldn't say "My hobby is ..." because we know the subject is hobbies. I'd say "I play tennis" or "I like to eat gourmet sushi" or "I go horse riding every Saturday" something like that.
Anyway for classroom use your sentences are fine.
The answers these threads so often generate make me feel despondent sometimes.
3. Both gerunds and infinitives can be used as the subject or the complement of a sentence. However, as subjects or complements, gerunds usually sound more like normal, spoken English, whereas infinitives sound more abstract. In the following sentences, gerunds sound more natural and would be more common in everyday English. Infinitives emphasize the possibility or potential for something and sound more philosophical. If this sounds confusing, just remember that 90% of the time, you will use a gerund as the subject or complement of a sentence.
Learning is important. normal subject
To learn is important. abstract subject - less common
The most important thing is learning. normal complement
The most important thing is to learn. abstract complement - less common
Thanks for your help. Now I understand native speakers wouldn't ask "What's your hobby?" and "Do you have any hobbies?" could be used.
Japanese people tend to misuse the word "hobby" because of its translation "趣味".