Fuel Tank Help 1997 Honda VFR

So I was pissed off because my VFR was leaking gas yet again and I assumed it was my carburetor which i had rebuilt last summer. I was not going to worry about it until next season, but when I was taking the battery out for winter today I noticed a little hose in front of the battery that seemed loose. I popped the tail fairing off and traced the little hose back to the gas tank. I noticed that the little hose was connected to the tank but there was a larger hose, I assume the fuel line, that was completely disconnected. So I have two questions... 1. Is the hose that is about 1CM in diameter my fuel line? And 2. What is the little hose for leaving the gas tank, just drainage in case of a crash? I am not a mechanic so please don't flip out. Thanks!

 

the small hose drains the pocket around the fuel filler hole of rain water or spilled fuel.