i dont know about the 450 watt...MH
usually only come in 400 which means if you put a 400 bulb in a 450 ballast you could blow up the bulb.
plus a batwing reflector is just a piece of metal bent in a reflector shape. its not a real hood, the growstore around here sells them for like $20, you cannot put a glass shield on them and you have to hang them from chains.
the ballast looks homemade also, thats not the typical shape.
i would at least get more pics, esp the tag on the balast that says who it was made by and what the actual wattage is.
just my 0.02$