In the DMG about playing on a grid we find:
The area of effect of a spell, monster ability, or
other feature must be translated onto squares or hexes to determine
which potential targets are in the area and which aren't. Choose an
intersection of squares or hexes as the point of origin of an area of
effect, then follow its rules as normal. If an area of effect is
circular and covers at least half a square, it affects that square.
Thus you will have to choose one of the 4 corners of the square you control as the point of origin. This effectively means that it can only cover a 2 square wide area in all cases and you get to choose to aim it right or left.
I would like to note that I personally would rule that you can aim it straight ahead, but would give those creatures whose squares are only half covered by the area Advantage on the saving throw.