If an elliptic race track is 100 yards long and 20 yards wide, then how far apart are the foci?

Question

a. 

b. 

c. 

d. 

Answer 1

For an ellipse: a²-b² = c² where a is the semi-major axis, b is the semi-minor axis and c is the focal length.

The foci are 2c apart, so the answer is

2sqrt( 50²-10²) which you can match with one of the answers.

Answer 2

an ellipse is 100 yds long 40 yards wide

how far apart are the foci??

semi major axis squared minus semi minor axis squared = focal length squared

50^2 - 20^2 = c^2 = focal length squared

c^2 = 2500-400 = 2100

c = 10sqr21

distance between the foci = 2c = 20sqr21= about 91.65 yards

none of the answers is correct

closest are 35sqr6 or 40sqr6, both off by about 6