Solve the problem.
-A window above a door is to be made in the shape of a semiellipse. If the window is 12 feet at the base and 4 feet high at the center, determine the distance from the center at which the foci are
Located. Round to one decimal place.
A) 11.3 feet
B) 20.0 feet
C) 4.5 feet
D) 8.9 feet

Question

Quizplus · Accepted Answer

The distance of the foci from the center in an ellipse is given by $c = \sqrt{a^2 - b^2}$, where $a$ is the semi-major axis and $b$ is the semi-minor axis. For a semiellipse with a base of 12 feet, the semi-major axis $a = \frac{12}{2} = 6$ feet, and the height (semi-minor axis) $b = 4$ feet. Plugging these into the formula gives $c = \sqrt{6^2 - 4^2} = \sqrt{36 - 16} = \sqrt{20} = 4.47$, which rounds to 4.5 feet.

Solve the Problem. -A Window Above a Door Is to Be Made in Be