Option 2 actually sounds very strange! ;) In correct English, it should be, "Would you happen to know where my book is?" You can understand the first sentence as, "You wouldn't happen to know where my book is, would you?"

Hi Vanessa, Option 1 is correct, though it is polite and archaic. In parts of the English speaking world we would say "You wouldn't happen to know...?" if we were having fun and want to sound posh (upper class) whilst still wanting to know where the item is. This is exactly the same as asking "Do you know...?" Option 2 is incorrect.

No doubt second one is correct but somewhat, first one is also correct. You could improve the first sentence like this.. You wouldn´t happen to know where my book is. Would you?

Option 1 is correct. It's formal but still very much in common use. Option 2 is definitely not right

Thank you very much Tom :)