Question

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

Answer 1

@DarkBlueChocobo come here to play, you are the right person to solve it. practice on other's problem is the best way to confirm your knowledge.

Answer 2

@juliamae10 since I saw you post 2 exactly- the- same problem on 2 different sections, I assume that you just want the answer. If it is so, why don't we let other student who needs practice work out on your problem, right? both you guys get what you want.

Answer 3

@Loser66 co vertices are they half of the vertices ?

Answer 4

@DarkBlueChocobo foci is about c, and it is on the vertical line, hence your main axis is y axix

Answer 5

Or am I getting mixed up between hyperbolas and parabolas

Answer 6

co-vertices is a minor one, not the long one

Answer 7

so the length of the minor axis 20?

Answer 8

40, not 20

Answer 9

you find a by c^2 = a^2 -b^2

Answer 10

hence a^2 =??

Answer 11

does c^2 = 8^2? @Loser66

Answer 12

yup

Answer 13

b^2=20^2?

Answer 14

yup again

Answer 15

8^2=a^2-20^2

Answer 16

yup

Answer 17

need a^2

Answer 18

so -a^2=400-64

-a^2=336

Answer 19

hey

Answer 20

Did i mess up with -a^2?

Answer 21

\(8^2 = a^2 -400\\a^2 = 8^2 +400\) just +400 both sides

Answer 22

ohhhh that was simple:

a=sqrt464

Answer 23

nope, let a^2 as it is. \(a^2 = 464\)

Answer 24

now, you have a^2, b^2, just plug all in formula for VERTICAL ellipse formula
that is \(\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1\)

Answer 25

\[\frac{ x^2 }{ 20^2}+\frac{ y^2 }{ 464^2 }=1\]

Answer 26

\[\frac{ x^2 }{ 400}+\frac{ y^2 }{ 464 }=1\]

Answer 27

And that would be the equation

Answer 28

Remember, if it is HORIZONTAL ellipse, then the denominator of x term is a^2
if it is VERTICAL ellipse, the denominator of x term is b^2
They are different, that is why at the beginning, I have to define which one is the correct form by using foci and co-vertices.

Answer 29

yes, that is the required equation.

Answer 30

Yes if the number is bigger under y that means that is it vertical

Answer 31

if the bigger number is under x it is horizontal

Answer 32

ok, good job

Answer 33

Thank you for leading me to solve it