The rectangular piece of property measures 10 mi by 4 mi. find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides.

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.