Articles (on a coast or on the coast)

5 years ago

 Hi!

"I live in (4) a relatively small town on (5) a / the coast, with a sizeable tourist influx in the summer months."

To choose the correct answer wasn't very difficult for me as I've heard tens of times (not hundreds) people say "on the coast." That said, I still don't understand the reason for using "the". Let's say there several coasts (west and east costs) and I am talking about one coast. So, I could say "I live on a coast, with a sizeable tourist influx in the summer months." 

Tell me please where I am wrong (1). Why can't I say "a cost" in this sentence? (2) Is there a case where I can say "on a coast" or I live "on a cost?" (3) 

Thank you!