Chapter 10.1, Problem 77PE

The Roman Coliseum is an elliptical stone and concrete amphitheater in the center of Rome, built between $70\text{ A}\text{.D}\text{.}$ and $80\text{ A}\text{.D}$ . 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 $287\text{ ft}$ and the maximum width is $180\text{ ft}$ . 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 $615\text{ ft}$ and the maximum width is $510\text{ ft}$

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.