Question

Find the center, vertices, and foci of the ellipse with equation x squared divided by four hundred plus y squared divided by two hundred and fifty six = 1

Answer 1

To solve this problem you must apply the proccedure shown below:

1. You have that the equation of the ellipse is the following:

(x²/400)+(y²/256)=1

2. You have that:

((x-0)²/400)+((y-0)²/256)=1

3. Then, the center is:

(0,0)

4. The vertices are:

a²=400
a=√400
a=20

(-20,0)
(20,0)

b²=256
b=√256
b=16

(0,-16)
(0,16)

5. The focci is:

a²–c²=b²
√(400-256)=c
c=12

(-12,0)
(12,0)