anonymous
  • anonymous
Write the equation for an ellipse with co-vertices (0,-3) and (0,3), major axis of length 10.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@jim_thompson5910 :)
jim_thompson5910
  • jim_thompson5910
where is the center?
anonymous
  • anonymous
idk.. it doesn't say... it just says what i typed in :/

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

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