Do I need another amp for a sub-woofer?

[Herbicidal]

I'm smack in the middle of sound deadening my car. I'm staying with the stock head unit for now and bought a 4-channel line output converter and I've replaced the stock speakers with Alpine Type R's (6x9) in the rear deck and Kicker component speakers with tweeters in the front door panels. I also bought and installed an Eclipse EA4200 4-channel amp, perhaps you knowledgeable people can take a look at the specs. To my ears, it sounds great! However, what I realize now is that I don't have much in the way of bass. Those of you 'in the know' probably are saying "DUH!" right about now. I've been looking at a pretty inexpensive sub woofer that another member bought and used with great success. It's a Bazooka-ELB110RS this is a 10" sub.

Questions: I admittedly don't fully understand the outputs on my Eclipse amp and whether I can use it to also power that sub? I'm not looking to blow out my windows, but I would like to round out the sound and right now I have great mids and highs, but no low's.

Did I blow it by buying a 4-channel LOC?
Should I bite the bullet and buy a higher quality LOC?
Would that gain me anything?
Do I need to get another amp just for the subwoofer?
If so, how would I connect it (maybe via the Eclipse amp)?

Man, I'm such a rookie with this stuff. Thanks in advance for the advice and help. Crap, I thought I was going to be happy with just replacing the stock speakers. Hopefully I didn't blow it with my previous purchases.