Did the Advance University help out?
If not, poke around here a bit, and you'll find many discussions of the HID nature!
BTW: Normally, a Capacitor is used to improve Power Factor from Nominal (50%) to High (±90%). This is the "Option" of the High Pressure Sodium "55 Volt Lamp" family, as are a few other low Wattage HIDs.
There are other uses of the Capacitor - such as with the High Reactance Autotransformers - where the Cap is driven on the Input side of Ballast, and with CWA's, it's a series element to the Reactor section. With Regulated Lag Ballasts, there's a seperate Capacitor Secondary Winding.
All these setups do not specify the Cap as "Optional".