iheartfood
Write the equation for an ellipse with co-vertices (0,-3) and (0,3), major axis of length 10.
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iheartfood
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@jim_thompson5910 :)
jim_thompson5910
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where is the center?
iheartfood
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idk.. it doesn't say... it just says what i typed in :/
jim_thompson5910
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i know, you have to find it
jim_thompson5910
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the co-vertices lie along the minor axis
iheartfood
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ok, how do we do that?
jim_thompson5910
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the midpoint of this minor axis is where the center is
iheartfood
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minor is vertical or horizontal?
jim_thompson5910
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(0,-3) and (0,3) lie on what line?
iheartfood
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so would the center be (0,0) ??
iheartfood
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the x-axis?
jim_thompson5910
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no, you have it flipped
iheartfood
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okay so how do i write this equation??
oh the y axis?
jim_thompson5910
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so the minor axis is vertical
jim_thompson5910
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the major must be horizontal
iheartfood
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ohh okay :) so its on the major axis?
jim_thompson5910
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what is
iheartfood
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(0,-3) and (0,3) ?
jim_thompson5910
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no they are on the minor axis because they are co-vertices
jim_thompson5910
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not vertices
iheartfood
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ohh okay i see... what do we do now??
jim_thompson5910
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how long is the minor axis?
iheartfood
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idk :/ how do i find that?? i just know the major axis is 10...
jim_thompson5910
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what's the distance between the co-vertices?
iheartfood
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6? so is 6 the length of the minor axis?
jim_thompson5910
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yes good
jim_thompson5910
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cut that in half to get 3
that's the length of the semi-minor axis
jim_thompson5910
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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
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so b = 3
jim_thompson5910
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you know the center is (0,0) because you just found this, so (h,k) = (0,0)
iheartfood
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okay :)
so far we have this?
(x-0)^2/(a^2) + (y-0)^2/(3^2)=1
??
jim_thompson5910
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good, the only thing you need is 'a'
iheartfood
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how do we find that? do we square root 10? if so, can i just write sq.rt.10?
jim_thompson5910
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no, the length of the major axis is 10
the length of the semi-major axis is ____
iheartfood
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5?
jim_thompson5910
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so a = 5
iheartfood
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okay so is this my final equation??|dw:1356131103670:dw| is that it?? or do i need to simplify it more?
jim_thompson5910
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you can simplify it more if you want
jim_thompson5910
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|dw:1356131176856:dw|
iheartfood
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but when it says write the equation, what format do they want it in?
jim_thompson5910
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there are many formats, but that's probably the best one
jim_thompson5910
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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
iheartfood
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the simplified version?
iheartfood
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kk so we are done now?? htats it?
iheartfood
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kk thank youu :)