I'm not even sure you really need the cap. You might get a better spark using one though. I don't believe it will do you a service if a poster just spells out a solution - the problem is supposed to get you to to reason it out for yourself. But here's a way to look at the problem -
A ballast is just an inductive device with one or more high-inductance windings. They usually also have one or more lower inductance, low voltage windings. Current through a winding will magnetize the core to some extent, and any change in that current will induce current to flow in all windings, as the increasing or collapsing magnetic flux lines pass through the turns of the windings. Your goal will be to coax the greatest current change possible, and to take the greatest advantage of that change. Remember also, that you can store energy in a cap. Good luck!