Question

What is the equation of the ellipse with co-vertices (-20, 0), (20, 0) and foci (0, -8), (0, 8)

Answer 1

@phi @iGreen @GenericNoodles @TheSmartOne

Answer 2

what is the center going to be ?

Answer 3

@phi i think 0,0 i wasnt told.

Answer 4

the center would be the average of the focuses or the average of the co-vertexes

Answer 5

add up the x's of the focuses, and divide by 2
(0+0)/2 = 0
then the y's
(-8+8)/2 = 0
so (0,0)

Answer 6

do you remember the formula to find the distance of the focus from the center?

Answer 7

No i dont @phi

Answer 8

you used it a few times to do your earlier problems. If you are doing this work, it makes sense to try to remember what you are doing.

if we call the distance from the center to the focus "c"
then
\[ c^2 = a^2 - b^2 \]
where a is the semi-major axis and b is the semi-minor axis

Answer 9

oh yeah lits pythagoream and theroem

Answer 10

its*

Answer 11

you remember that the focus lies on the major axis, right?
we don't know the length of the semi-major axis.
but we do know the length of the other axis. what is it ?

Answer 12

remember vertex is the extreme edge of the ellipse.
the length from the center to the co-vertex is what we want.

Answer 13

oh so how do i find it

Answer 14

you read the question. they tell you.

Answer 15

im kind of confused and the clock is running out on this assaignment. i have 10 mins left

Answer 16

is it 20?

Answer 17

yes, the semi minor axis is 20. i.e "b" is 20
now fill in what you know about
\[ c^2 = a^2 - b^2 \]
do you know what the distance is from the center to the focus is ? that is "c"

Answer 18

c= 8

Answer 19

ok. and b is 20
can you find "a" ? or just a^2 ?

Answer 20

how would i find a? we used up what was given to us in the questions

Answer 21

then use the formula
\[ \frac{y^2}{a^2} + \frac{x^2}{b^2} = 1 \]
to write down the equation

Answer 22

c^2= a^2 - b^2
put in the numbers for b^2 and c^2

Answer 23

64= a^2 - 400

Answer 24

now add +400 to both sides

Answer 25

you get
400+64 = a^2 +400 -400
or
464= a^2

use that and b^2= 400 in
\[ \frac{y^2}{a^2} + \frac{x^2}{b^2} = 1 \]

Answer 26

@phi so which one would it be in the answers?. a^2= 464 and b^2 = 400 so it would be B ?