Since it's after the meter, I do not believe the Utility Company will come out and find the line for you. They only do that for their lines.
Odds are very good that the line is the shortest distance between both buildings. I would pick a building, either one, and figure out where the line is coming into that building. It will mean some shovel work, and maybe even removing what's on the wall.
Is this a dedicated line from a breaker? Is there anything else on that line? like an outlet on the outside of your house? If it was run after the house was built, a lot of people will put an outlet on the outside of the house, then dig the trench from there to the barn.
Thanks, this put a smile on my face. Ideally, sure.
But...the farm we had as a kid had galvanized water pipes with lots of bends in them, and when there was an issue, we had to dig end to end because there was no accounting for the path it took. I strongly suspect the original farmer used bent left over pipe from somewhere else, and played with the pipe to get from "A" to "B". That experience taught me to be careful about assuming. A great life lesson for me.
On this ranch, the reason that I bought a locator beyond the "assuming issue", was the power line from the barn. I was worried about where it might go because I had a couple of projects involving excavation, one deep, one not.
Standing at the barn, there was an easy due south then west line. It would have been parallel to a barn wall, then crossed one driveway at a 90, then continued 30', made a second 90 and gone straight to the house. The original water line did something close to that.
But no...
The line that I was concerned about actually headed from the barn (which runs E-W) due west for about 120', which is away from the house, crossing one access road along about the longest possible crossing path, then went under a guard rail that could have been avoided if the line turned south 8' sooner, having gone under the guard rail headed S, in a not entirely straight line, for 110', under the driveway the whole time, and then takes a 45 degree bend to head south west to head under a small retaining wall, a larger retaining wall, then some stairs, for another fifty feet, and then skirts a 2'x2' masonary column, where it turns due S, before eventually turning W to meet the house. Total length is probably double what the "nice" route might have been and about 3X the straight line route.
Did I mention that I was very happy to have bought a locator?
My takeaway is that there is what the plan has, and there is what someone actually did on the day, which depending on the locale, the person, and the subsurface conditions may be something else again. I have no insights to the chosen route. It seems bad from any angle I can think of, except it might have allowed a NEC minimum burial depth for most of the run, but at the cost of twice the conduit and twice the wire.
YMMV... so my takeaway for me is to buy or rent a locator, or be willing to take care of the consequences.

All the best,
Peter