If you mean Egyptian settlement as opposed to Egyptian power, the eastern boundary was the copper mines of Sinai or the negev. The southern boundary was a fort on the Nile on the border with Nubia. The northern boundary was the Mediterranean, the western boundary was the Great Oasis or the border with the kushite or Libyan realm.
Northern - Mediterranean Sea.
Eastern - dessert
Western Red Sea and dessert.
Look at a map and see where Egypt is. In practice, much of Egypt is a tiny strip of cultivated land both sides of the Nile river, not more than 10 miles wide, but many hundreds of miles long. The remainder is dessert.
