The rectangular piece of property measures 8 mi by 6 mi. find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides

The ellipse will be inscribed in the rectangle.

Because the rectangle measures 8 mi by 6 mi, the ellipse has

a = 8/2 = 4 mi (major axis)

b = 6/2 = 3 mi (minor axis)

The equation for the ellipse is

x^2/a^2 + y^2/b^2 = 1

That is

x^2/4^2 + y^2/3^2 = 1

x^2/16 + y^2/9 = 1

Answer:

x^2/16 + y^2/9 = 1