I am sorry, you are misinformed about the Sanskrit meaning of the word Parth. pArtha actually simply means related to or son of or descendant of pRthA, and could simply refer to a king. Mythologically, however, pRthA is indeed the mother of arjuna, the hero to whom you refer, and who was an excellent archer.
pRthA comes from the root prath which meant to extend. The only meaning of that word extant in later language is a spread of hand, but related words mean expanse of land, or the whole world, and is ultimately cognate with English words like plate.