Solve the Problem $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 4 } = 1$

Solve the problem.
-An elliptical riding path is to be built on a rectangular piece of property that 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

A) $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 4 } = 1$
B) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 4 } = 1$
C) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$
D) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 100 } = 1$