How far apart are the foci of an ellipse with a major axis of 10 feet and a minor axis of 6 feet?

Solution:

The ellipse is represented by the diagram below:

The major axis 2a of the ellipse = 10 feet. (Given)

The minor axis 2b of the ellipse = 6 feet (Given)

Since 2a = 10 feet, implies

a = 5 feet

Also 2b = 6 feet, implies

b = 3 feet

To find the coordinate of the foci we have to use the following relationship:

b² = a² - c²

(3² = (5)² - c²

c² = 25 - 9

c² = 16

c = ± 4

Therefore the foci are located at 4 feet on either side of the centre of the ellipse. Therefore the foci are 4 + 4 = 8 feet apart.

How far apart are the foci of an ellipse with a major axis of 10 feet and a minor axis of 6 feet?

Summary:

The Major Axis is 2a =10 feet; the minor axis is 2b = 6 feet and hence c = 4 feet. The distance between the foci is 2c which is 8 feet.