It depends on your API but I would create a separate web and api instance and have them connect to the same database.
It's more of a feeling, having 2 systems operation in the same install sounds tricky, though you might have to do more work.
If your API is merely a presenter of your data then it would be ok to have it in one install, if your API is doing other stuff than your web install is then 2 separate systems would be my anwser.
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