A rectangular board is 2 feet by 12 feet. How far from the center of the board will the foci be located to determine the largest elliptical tabletop? Round your answer to the nearest tenth.
A) 1.0 ft
B) 5.9 ft
C) 0.1 ft
D) 5.0 ft

Question

Quizplus · Accepted Answer

The foci of an ellipse are located along the major axis, which in this case is the longer side of the rectangle, 12 feet. The distance from the center to each focus (c) can be found using the formula c = sqrt(a^2 - b^2), where 2a is the length of the major axis and 2b is the length of the minor axis. Here, a = 12/2 = 6 feet and b = 2/2 = 1 foot. Thus, c = sqrt(6^2 - 1^2) = sqrt(36 - 1) = sqrt(35) ≈ 5.9 feet.

A Rectangular Board Is 2 Feet by 12 Feet