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

Question

anonymous · Answer

@jim_thompson5910  :)

jim_thompson5910 · Answer

where is the center?

anonymous · Answer

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

jim_thompson5910 · Answer

i know, you have to find it

jim_thompson5910 · Answer

the co-vertices lie along the minor axis

anonymous · Answer

ok, how do we do that?

jim_thompson5910 · Answer

the midpoint of this minor axis is where the center is

anonymous · Answer

minor is vertical or horizontal?

jim_thompson5910 · Answer

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

anonymous · Answer

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

jim_thompson5910 · Answer

yep

anonymous · Answer

the x-axis?

jim_thompson5910 · Answer

no, you have it flipped

anonymous · Answer

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

jim_thompson5910 · Answer

so the minor axis is vertical

jim_thompson5910 · Answer

the major must be horizontal

anonymous · Answer

ohh okay :) so its on the major axis?

jim_thompson5910 · Answer

what is

anonymous · Answer

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

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

not vertices

anonymous · Answer

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

jim_thompson5910 · Answer

how long is the minor axis?

anonymous · Answer

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

jim_thompson5910 · Answer

what's the distance between the co-vertices?

anonymous · Answer

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

jim_thompson5910 · Answer

yes good

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

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 · Answer

so b = 3

jim_thompson5910 · Answer

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

anonymous · Answer

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

jim_thompson5910 · Answer

good, the only thing you need is 'a'

anonymous · Answer

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

jim_thompson5910 · Answer

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

anonymous · Answer

5?

jim_thompson5910 · Answer

so a = 5

anonymous · Answer

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