The Roman Coliseum is an elliptical stone and concrete amphitheater in the center of Rome, built between 70 a.d. and 80 a.d. The Coliseum seated approximately 50,000 spectators and was used among other things for gladiatorial contests.

a. Using a vertical major axis, write an equation of the ellipse representing the center arena if the maximum length is 287 ft and the maximum width is 180 ft. Place the origin at the center of the arena.

b. Approximate the eccentricity of the center arena. Round to 2 decimal places.

c. Find an equation of the outer ellipse if the maximum length is 615 ft and the maximum width is 510 ft.

d. Approximate the eccentricity of the outer ellipse. Round to 2 decimal places.

e. Explain how you know that the outer ellipse is more circular than the inner ellipse.