From the measures of the hallway you know about the ellipse:

semi-major axis : 2.5 m

semi-minor axis : 1 m

coordinates of the center: C(0, 3)

Thus the equation of the ellipse is:

Because you only need the upper part of the ellipse you can solve for y to get the equation of a function:

The points A and B are 1 m from the wall: A(-1.5, e(1.5)) and B(1.5, e(1.5))

Because the ellipse is symmetric about the y-axis it is only necessary to calculate e(1.5).

I've got A(-1.5, 3.8), B(1.5, 3.8)