What is the term used to refer to an imaginary line that separated white settlements and Indian settlements?
Since you have tagged this with "Lousiana Purchase and the Opening of the West," I assume that you are talking about a time in US history rather than about the line drawn by the British with the Proclamation of 1763.
If that is the case, I believe that the term you are looking for is "frontier." The frontier should not be imagined, though, as a line that ran, like a city limit line or a state line, between white settlements and Indian settlements that were right next to each other. Instead, the frontier should be seen as a general area where the farthest-out of the white settlements ended. The frontier was an area that kept moving farther and farther west as the white settlers pushed out into the Louisiana Purchase.