A rectangular board is 9 by 17 units A string is connected t

A rectangular board is 9 by 17 units. A string is connected to the foci and pulled taut by a pencil in order to draw the ellipse. Find the length of the string

Solution

length of major axis = 2a = 17

a = 17/2 = 8.5

length of minor axis = 2b = 9

b = 4.5

foci c^2 = a^2 - b^2

c^2 = 8.5^2 - 4.5^2 = 52

c = 7.21

length of the string = two times foci = 2*7.21 = 14.42 units