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Here is what I have:
Macbook air (MacBookAir3,2) running 10.10.2 Apple TV (A1469) 3rd gen
I have airplayed my iPad to my TV numerous times so I know it works. However, airplay does not even show up as a display option on my mac.
I have been hunting on the net for an hour and it isn't clear that it simply isn't supported by my mac.
So: Can anyone tell me how to do this or conclusively state it isn't possible/