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)