Solve the problem.
-A rectangular board is 14 by 20 units. How far from the short side of the board will the foci be located to determine the largest elliptical tabletop?
A) $7.0$
B) $7.1$
C) $2.9$
D) $3.0$

Question

Quizplus · Accepted Answer

The largest ellipse that can fit inside a rectangle will have its major axis equal to the longer side of the rectangle (20 units) and its minor axis equal to the shorter side (14 units). The semi-major axis $a = 10$ and the semi-minor axis $b = 7$. The distance of the foci from the center is given by $c = \sqrt{a^2 - b^2} = \sqrt{10^2 - 7^2} = \sqrt{51} \approx 7.14$. Since the ellipse is centered, the distance from the short side is $10 - \sqrt{51} \approx 2.86$, which rounds to 2.9.

Solve the Problem 7.07.07.0 B) 7.17.17.1 C) 2.92.92.9 D) 3.03.03.0

Solve the Problem $7.0$ B) $7.1$ C) $2.9$ D) $3.0$