what if i pass focus to my opponent

Yes — passing Focus hands Focus and Priority to your opponent, and the Showdown only ends if they also pass (Rule 348 / FAQ 12802).

Until then they can play an Action or Reaction, activate an ability, or pass back. If they play something and it resolves, Focus doesn't come back to you as a "pass" — it automatically moves to the next player in turn order once the chain is empty and the state returns to Open (Rule 346), so the showdown continues as long as anyone keeps acting.

Two quick notes: the pass that counts toward ending a showdown is the Pass action taken with an empty chain, not passing Priority mid-chain (FAQ 218). And if it was a Combat Showdown, two passes sends you to Combat Damage and then Combat Cleanup; a Non-Combat Showdown has no damage step and goes straight to Control/Conquer for the sole player left there.