PreCalc (ellipse) math problem?

Question

1. Find the distance bewtwen the foci of an ellipse that has a major axis of length 20 and a minor axis of length 16.

2. Find the length of the major axis of an ellipse that has the distance between the foci equal to 10 and the length of the minor axis equal to 24.

Answer 1

1.

The length of major axis 2a = 20

                                        a = 10

The length of minor axis 2b = 16

                                         b = 8

But c² = a² - b²

c is the distance between the foci of an ellipse

Substitute a = 10 and b = 8 in the formula c² = a² - b²

c² = 10² - 8²

c² = 100 - 64 = 36 =6²

Therefore c = 6

The distance between the foci of an ellipse : c =  6.

 

Answer 2

2.

The length of major axis 2a

The length of minor axis 2b = 24

                                         b = 12

But c² = a² - b²

c is the distance between the foci of an ellipse c = 10

Substitute c = 10 and b = 12 in the formula c² = a² - b²

10² = a² - 12²

100= a² - 144

a² = 100 + 144

a² = 244

a = √(244)

The length of major axis of an ellipse : 2a = 2√(244).