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In Ender's game, right after the Second Invasion, the International Fleet's main secret strategy was

sending out ships to the Formic home world as soon as they had a working ansible.

However, how did they know where that was? Remember, it was dozens of light years away, and even if they had the general direction, when traveling such distances across galaxies you can't just guess and hope you get the exact angles you'd need.

Edit

From chapter 13 of Ender's game: relevant point in bold

“What’s all the secrecy for, anyway?” “Because we've taken some terrible risks, Ender, and we don’t want to have every net on earth second-guessing those decisions. You see, as soon as we had a working ansible, we tucked it into our best starships and launched them to attack the buggers home systems.” “Do we know where they are?” “Yes.” “So we're not waiting for the Third Invasion.” “We are the Third Invasion.”

  • Did you read Ender's Shadow? – C.B. Oct 31 '13 at 23:28
  • @C.B. No, just Ender's game, Ender in Exile,First Meetings, and Mazer in Prison so far. – ike Oct 31 '13 at 23:31
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    Then i'm not going to spoil it for you, but i believe this question is partially answered in Ender's Shadow (chapter 21). Not a perfect answer, but for me it was still quite good. – C.B. Nov 1 '13 at 0:15
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    @CB - make it an answer and use spoiler format (">! ") – DVK-on-Ahch-To Nov 1 '13 at 2:05
  • @C.B. - I just checked Chapter 21 - the only thing I saw was Nikolai's suggestion to Bean that they may have FTL communications that Bean didn't think of before. Didn't go into how they found the worlds, except for the negative (no light to follow back from communications). – DVK-on-Ahch-To Nov 1 '13 at 2:37
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I don’t think there are any major spoilers here, but if others think otherwise feel free to hide, and remove this comment.

Give the edit to the question we know, that the destination was the “home systems” not the “Formic home world”. The bugs found Earth during expansion where our sphere and their sphere overlapped. Additionally the bugs did not consider humanity intelligent, so they had no reason to attempt deceit in return.

Departing trajectories would tend to point towards the center of their sphere, and all things being equal their home world would tend to be at or near the center of the average trajectory. The exact location of the “Formic home world” need not be defined when we man first started after the bugs, it could be estimated very early in the conflict and the final target chosen as the battle progressed, as is already know man has a working ansible so coordination would not be problematic.

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