Question

PLEASE ANSWER ASAP!!

A carpenter wants to cut the largest possible ellipse from a 5 feet by 11 feet rectangular board. After the foci are located, a string is connected to them and pulled taut by a pencil in order to draw the ellipse. Find the length of the string.

Answer 1

Explanation:

The largest possible ellipse will have a semi-minor axis of 2 feet and a semi-major axis of 4 feet. If we center the board on the origin of the cartesian coordinate plane, we can derive the location of the foci and thus, the length of string he will need:

x^2 / 16 + y^2 / 4 = 1

Vertices:

(-4 , 0) , (4 , 0)

(0 , -2) , (0 , 2)