Hd4870 on my resolution?

It doesn't matter whether its a TV or a computer monitor, resolution is resolution. No matter how big or small or how many the pixels are, they're still pixels and they require the same amount of graphics processing to fill. For example, a 24" computer monitor with a resolution of 1920x1080 and a 42" TV screen with a resolution of 1920x1080 would take the same exact requirements to run. If your TV's resolution is that low, this card will do just fine. In fact, you could do just about anything with that.