Solve.
-A rectangular board is 2 ft by 12 ft. How far from the center of the board should the foci be located in order to cut the largest elliptical tabletop from the board?
A) 1.0 ft
B) 5.9 ft
C) 0.1 ft
D) 5.0 ft

Question

Quizplus · Accepted Answer

The largest elliptical tabletop that can be cut from the board will have its major axis along the length of the board (12 ft) and its minor axis along the width (2 ft). The distance between the center of the ellipse and each focus (f) can be found using the formula $f = \sqrt{a^2 - b^2}$, where $a$ is half the length of the major axis and $b$ is half the length of the minor axis. Here, $a = 6$ ft and $b = 1$ ft, so $f = \sqrt{6^2 - 1^2} = \sqrt{35} \approx 5.9$ ft.

Solve. -A Rectangular Board Is 2 Ft by 12 Ft. How