Question

Find the standard form of the equation of the ellipse and find the center. Given the vertices:(0,+-8); Foci: (0,+-4)

Answer 1

If the vertices are (0,8) and (0,-8), where is the center?

Answer 2

(0,0)

Answer 3

Exactly.

Answer 4

And what is the value of "a"

Answer 5

8?

Answer 6

yes. And do you know that the distance from the center to the focus is "c" ?

Answer 7

yes

Answer 8

So "c" is ???

Answer 9

so you do c^2=a^2-b^2?

Answer 10

yes

Answer 11

And remember that the major axis is vertical so a^2 goes under y^2

Answer 12

but since the foci is given...c=-+2

Answer 13

The focal point is (0,4) so c = 4

Answer 14

oh you square the 2

Answer 15

Where did you get 2?

Answer 16

so what goes under x^2?

Answer 17

c is the distance from the center to the focal point. If the center is (0,0) and the focal point is (0,4), then c has to be 4

Answer 18

oh ok

Answer 19

16=64-b^2
-48=-b^2
48=b^2

Answer 20

major axis is the same as vertices?

Answer 21

The major axis is the distance between the vertices and its length is 2a

Answer 22

so b=sqrt48

Answer 23

Yes.