Not a real tragedy, but you can't run the engine till you fit a new hose. You cannot fix these -I've tried and it's impossible.
bad hose like a pin hole or bad clamp
I would say you have a bad water pump, thermostat or a bad hose depending on where the antifreeze is spraying from. If the antifreeze is coming from the timing cover area you have a bad pump, if it is coming from the front area of the motor I would say bad hose, if you are hearing a gurgling sound from the radiater I would say bad thermostat.
You would lose the water/antifreeze mix in the system of course. If you think the hose or hose's are bad replace them.
get a new hose
It is possible that the antifreeze is coming from a bad water pump. Clean the engine off. Watch it to see where the antifreeze is leaking from, as it could be a hose instead of the pump.
could be a bad hose, bad radiator, bad gaskets, bad Head... find out if there is antifreeze leaking, and where from. if there isn't a visible leak, check your overflow for engine oil if the overflow is black, then it's a blown head gasket, and you;r out some bucks.
Yes, busting a blood vessel can be really bad. Because you can lose a lot of blood and be in risk of dying.
Failed hose?
May have a bad heater coil or a lose coolant hose clamp near fire wall.
Depending on the area of the leak, it could be a bad head gasket, cracked head, bad gasket on any of the housings that control the antifreeze flow i/e thermostat, water pump etc, cracked or loose hose or bad water pump.
If the hose is leaking, replace it.
Water pump or bad hose clamp