Find the eccentricity e of the ellipse.
-A rectangular board is 8 units by 12 units. How far from the long side of the board will the foci be located to determine the largest elliptical tabletop?
A) 2.0 units
B) 4.5 units
C) 1.5 units
D) 4.0 units

Question

Quizplus · Accepted Answer

The semi-major axis (a) is 6 units and the semi-minor axis (b) is 4 units. The eccentricity e is calculated using the formula e = sqrt(1 - (b^2/a^2)) = sqrt(1 - (16/36)) = sqrt(20/36) = sqrt(5/9) ≈ 0.745. The distance from the center to each focus is ae = 6 * 0.745 ≈ 4.47 units, which is approximately 1.5 units from the long side (6 - 4.47 = 1.53).

Find the Eccentricity E of the Ellipse