If an encounter card requires me to discard a card under my control, can I choose to discard from my hand or my in-play area?
Cards in your hand are not in play, and cannot be discarded in this way. For example, if the mythos card says "discard 1 asset you control", it must be under the investigator's control (so on the table).

This is from the FAQ, under Rules Errata:


  Rules Reference page 7, column 1, “Costs” The third bullet point
  should read: “When a player is exhausting, sacrificing, or otherwise
  using cards to pay costs, only cards that are in play and under that
  player’s control may be used...”