Write the equation for an ellipse with co-vertices (0,-3) and (0,3), major axis of length 10.

- anonymous

Write the equation for an ellipse with co-vertices (0,-3) and (0,3), major axis of length 10.

- jamiebookeater

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- anonymous

@jim_thompson5910 :)

- jim_thompson5910

where is the center?

- anonymous

idk.. it doesn't say... it just says what i typed in :/

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## More answers

- jim_thompson5910

i know, you have to find it

- jim_thompson5910

the co-vertices lie along the minor axis

- anonymous

ok, how do we do that?

- jim_thompson5910

the midpoint of this minor axis is where the center is

- anonymous

minor is vertical or horizontal?

- jim_thompson5910

(0,-3) and (0,3) lie on what line?

- anonymous

so would the center be (0,0) ??

- jim_thompson5910

yep

- anonymous

the x-axis?

- jim_thompson5910

no, you have it flipped

- anonymous

okay so how do i write this equation??
oh the y axis?

- jim_thompson5910

so the minor axis is vertical

- jim_thompson5910

the major must be horizontal

- anonymous

ohh okay :) so its on the major axis?

- jim_thompson5910

what is

- anonymous

(0,-3) and (0,3) ?

- jim_thompson5910

no they are on the minor axis because they are co-vertices

- jim_thompson5910

not vertices

- anonymous

ohh okay i see... what do we do now??

- jim_thompson5910

how long is the minor axis?

- anonymous

idk :/ how do i find that?? i just know the major axis is 10...

- jim_thompson5910

what's the distance between the co-vertices?

- anonymous

6? so is 6 the length of the minor axis?

- jim_thompson5910

yes good

- jim_thompson5910

cut that in half to get 3
that's the length of the semi-minor axis

- jim_thompson5910

since the minor axis is vertical, this value of 3 corresponds to the value of b (which is paired with the y term below)
(x-h)^2/(a^2) + (y-k)^2/(b^2) = 1

- jim_thompson5910

so b = 3

- jim_thompson5910

you know the center is (0,0) because you just found this, so (h,k) = (0,0)

- anonymous

okay :)
so far we have this?
(x-0)^2/(a^2) + (y-0)^2/(3^2)=1
??

- jim_thompson5910

good, the only thing you need is 'a'

- anonymous

how do we find that? do we square root 10? if so, can i just write sq.rt.10?

- jim_thompson5910

no, the length of the major axis is 10
the length of the semi-major axis is ____

- anonymous

5?

- jim_thompson5910

so a = 5

- anonymous

okay so is this my final equation??|dw:1356131103670:dw| is that it?? or do i need to simplify it more?

- jim_thompson5910

you can simplify it more if you want

- jim_thompson5910

|dw:1356131176856:dw|

- anonymous

but when it says write the equation, what format do they want it in?

- jim_thompson5910

there are many formats, but that's probably the best one

- jim_thompson5910

because you can tell it's an ellipse and you can use it to read off the center, major axis, minor axis lengths, etc etc

- anonymous

the simplified version?

- jim_thompson5910

yeah

- anonymous

kk so we are done now?? htats it?

- jim_thompson5910

yes

- anonymous

kk thank youu :)

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