Solve the problem.
-A rectangular board is 2 feet by 18 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) 8.9 ft
B) 8.0 ft
C) 1.0 ft
D) 0.1 ft

Question

Quizplus · Accepted Answer

The foci of an ellipse are located along the major axis, which in this case is the length of the board (18 feet). The distance from the center to each focus (f) 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, $a = 9$ ft (half of 18 feet) and $b = 1$ ft (half of 2 feet). Plugging these into the formula gives $f = \sqrt{9^2 - 1^2} = \sqrt{81 - 1} = \sqrt{80}$, which is approximately 8.9 feet.

Solve the Problem. -A Rectangular Board Is 2 Feet by 18 Feet. How