this is the word problem: a stadium is to be built with stands in the form of two concentric ellipses. The outer ellipse is to be 240 yds long and 200 yds wide. The inner ellipse is to be 200 yds long and 100 yds wide. The football field of standard dimensions is to be laid out in the center of the inner ellipse.
I sketched this ellipse with the outer coordinate (240,200) and the inner coordinate (200, 100). I found the equations...outer: (x^2/120^2)+(y^2/100^2)= 1 AND inner: (x^2/100^2)+(y^2/50^2)= 1. I found those numbers because the outer a is 120 and outer b is 100. also the inner a is 100 and inner b is 50.
With all this information I found the inner area and outer area.
Inner: \pi (100)(50)= 15707.96 AND outer: \pi (120)(100)= 37699.11
Next I have to find the clearance will there be between the field and the inner ellipse in the direction of the end line. Im not sure where to begin at this step..