Of course you need to ask. By asking a teacher knows that you are applying for a job or going on to college. Teachers and professor have better uses of their time to write letters of recommendation to say MIT if you are not applying to MIT.
I still remember my classmates, 2 of them saying, they’re going to state and our lazy teacher said I’ll think about it’. When I said, I needed it for my Stanford application, he said he’ll give it to me the next day.