Question

The length of the major axis of the ellipse 16x² + 25y^2 = 400 is​

Answer 1

Step-by-step explanation:

ANSWER

For an ellipse of the form:

a

2

x

2

+

b

2

y

2

=1 (a>b>0)

Length of major axis: 2a

Length of minor axis: 2b

Eccentricity (e):

1−

a

2

b

2

Foci: (±ae,0)

Vertices: (±a,0)

Given ellipse:

16x

2

+25y

2

=400⟹

25

x

2

+

16

y

2

=1

Therefore, a=5,b=4

Now,

Length of major axis: 2a=10

Length of minor axis: 2b=8

Eccentricity (e):

1−

a

2

b

2

=

5

3

Foci: (±3,0)

Vertices: (±5,0)