2000 Yamaha Big Bear
 

I Have a 2000 Yamaha Big Bear 400 that has a hose coming off the bottom of the carb that is leaking gasoline

It is your overflow. turn your gas off on the petcock your needle is sticking in your carb. time for a rebuild kit.

It is often a bit of grit that has got in with the fuel and jammed the float valve open. If you turn the tap off and run the engine until the carb is dry, then turn the fuel on again, the flush of fuel may dislodge the grit. If that doesn't work you will have to remove the float bowl and clean it properly. May be the tiny plunger spring in the float needle is weak or the plunger sticking, only cure for that is a new needle.

Install a inline filter too if you have not already.