I realize I'm rather far out of my depth here, but when discussing asymmetric encryption, doesn't this typically imply the discussion is about authentication?

I realize I'm rather far out of my depth here, but when discussing asymmetric encryption, doesn't this typically imply the discussion is about authentication? Is there a way to derive the ephemeral keys? My understanding is that these are not directly shared, but it's exactly where I am weakest on the basic concepts of the handshake and related stuffs.