Question

How far apart are the foci of an ellipse with a major axis of 34 feet and a minor axis of 16 feet?

Answer 1

The answer is 30 feet. 

Answer 2

The foci of an ellipse are (c,0) & (-c,0)

Where c² = a² - b²

The major axis is 34 feet

So 2a = 34

Dividing by 2 on both sides

a = 17

Also minor axis is 16 feet

So 2b = 16

Dividing by 2 on both sides

b = 8

Now we know

c² = a² - b²

c² = 17² - 8² = 289 - 64 = 225

Taking square root on both sides

c = 15 feet

Now the two foci are (15,0) & (-15,0)

Distance between these points is 15 - (-15) = 15 + 15 = 30

The distance between the two foci is 30 feet.