Oscar Corporation is planning to construct an elliptical gate at its headquarters. The width of the ellipse will be 5 feet across and its maximum height along the center will be 3 feet. The company wants to place two bright spots at the foci of the ellipse. How far from the center of the ellipse will the spots be located?

Draw the elliptical gate and show the foci, the width, and height as in the figure below.

Note that

a = 5 ft, the width

b = 3 ft, the height

The center is at (0,0).

The foci are at (c, 0) and at (-c, 0).

The foci are related to a and b by

c² = a² - b²

= 5² - 3² = 16

c = + 4 or - 4

Answer:

The foci are located 4 ft horizontally from the center of the ellipse.