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

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where is the center?
idk.. it doesn't say... it just says what i typed in :/

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Other answers:

i know, you have to find it
the co-vertices lie along the minor axis
ok, how do we do that?
the midpoint of this minor axis is where the center is
minor is vertical or horizontal?
(0,-3) and (0,3) lie on what line?
so would the center be (0,0) ??
the x-axis?
no, you have it flipped
okay so how do i write this equation?? oh the y axis?
so the minor axis is vertical
the major must be horizontal
ohh okay :) so its on the major axis?
what is
(0,-3) and (0,3) ?
no they are on the minor axis because they are co-vertices
not vertices
ohh okay i see... what do we do now??
how long is the minor axis?
idk :/ how do i find that?? i just know the major axis is 10...
what's the distance between the co-vertices?
6? so is 6 the length of the minor axis?
yes good
cut that in half to get 3 that's the length of the semi-minor axis
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
so b = 3
you know the center is (0,0) because you just found this, so (h,k) = (0,0)
okay :) so far we have this? (x-0)^2/(a^2) + (y-0)^2/(3^2)=1 ??
good, the only thing you need is 'a'
how do we find that? do we square root 10? if so, can i just write sq.rt.10?
no, the length of the major axis is 10 the length of the semi-major axis is ____
so a = 5
okay so is this my final equation??|dw:1356131103670:dw| is that it?? or do i need to simplify it more?
you can simplify it more if you want
but when it says write the equation, what format do they want it in?
there are many formats, but that's probably the best one
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
the simplified version?
kk so we are done now?? htats it?
kk thank youu :)

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