I sifted through a number of sites, and all, seem to give a "D'var Torah", so there doesn't appear to be anything "authritative". However, this article seems to give the most "direct" answer, I think:
As to the future – that can found in just one word. The word is
‘ba’ama’ and occurs several times in chapter 35 verse 5. It is a
measurement and in itself does not seem so significant. ‘You shall
measure two thousand ama to the east…’ However, the first occurrence
of this word has a unique musical note attached to it. Found nowhere
else in the Bible, it is known as ‘karnei parah’ - the horns of a cow
–and that is rather what it looks like. The text commands us to
measure out an area around each city. Why? For the cattle of course!
That is what the note tells us. From the beginning the Israelites had
cattle. Pharaoh’s words after the tenth plague, when he finally
agrees to let the people go are ‘Take your flocks and your herds and
be gone.’ (Exodus 12:32) ‘And they went – and a mixed multitude with
them, and flocks and herds and very many cattle. (Exodus 12:38). Last
weeks parashah described the first act of settlement – the
apportioning of land outside Israel to the tribes of Reuven and Gad
and to half of the tribe of Menasseh precisely because they had so
As for the 2nd part of your question, why just THAT direction, I surmise some ideas.
- It happens to be the first direction mentioned. (I know that's an overly-simplified answer, but it may really not be more complex than that.)
- It may have something to do with the other trope groupes that follow in this verse. Yerach ben Yomo / Karnei Parah are considered "4th-level disjunctives" (See this wikepedia item that explains the trope rules and groupings.
- The easterly direction, which in this case, is the one mentioned first, is often the most "important" direction in the Torah for that is where the sun rises, and indicates the beginning of the new "day" (daylight, that is, not the calendar day.)
This wikipedia article has another explanation on why this word has a Karnei Parah. It's not my personal favorite, but you may enjoy it.