anonymous
  • anonymous
Find the equation of the Ellipse given the vertex (0,8) and (0,-8) ; and its eccentricity 3/4
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Hi!!
anonymous
  • anonymous
@mathmate
anonymous
  • anonymous
what i know \[\frac{ x^2 }{ a^2 }+\frac{ y^2 }{ b^2 }=1\]

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anonymous
  • anonymous
with the eccentricity being 3/4 this means c=3
anonymous
  • anonymous
and b=4 or is it a=4?
anonymous
  • anonymous
but its that the focus points u have there ?
anonymous
  • anonymous
so the vertex is the focus points?
mathmate
  • mathmate
oh, my bad, I didn't read the question well! yes, so b=8. and e=3/4=sqrt(1-a^2/b^2) since the major axis is vertical. So can you solve for a?
mathmate
  • mathmate
Also, e=3/4=c/b, so we can solve for c=3/4*b=6
mathmate
  • mathmate
|dw:1446858852098:dw|
anonymous
  • anonymous
ok the major axis is the y axis which gives an eccentricity of c/(major axis) ...c/b so i taught c would =3 and b=4 so b^2=16 c^=b^2-a^2 9=16-a^2 a^2=-9+16 a^2=7 a=sq.rt 7
mathmate
  • mathmate
The semi-major axis is 8, so b=8.
mathmate
  • mathmate
|dw:1446859343241:dw|
mathmate
  • mathmate
b=8, c=(3/4)*8=6 a^2=sqrt(b^2-c^2)=...
anonymous
  • anonymous
ok so c=6?
mathmate
  • mathmate
and a=?
anonymous
  • anonymous
a^2=28
anonymous
  • anonymous
a=sq.et 28
mathmate
  • mathmate
Yes, a=sqrt(28), exacly, or sqrt(28)=sqrt(2^2*7)=2sqrt(7). Both are good. So now you know both a and b, can you figure out the equation of the ellipse?
anonymous
  • anonymous
so the equation is x^2/28+(y-8)^2/64=1
mathmate
  • mathmate
Yes, that is correct. We do, however, write it as x^2/a^2 + y^2/b^2 =1 so take the square-roots and write it as: x^2/(sqrt(28)^2 + y^2/8^2=1
mathmate
  • mathmate
Sorry, I didn't see the (y-8)^2, there is no translation. so it should read just y^2. See the diagram I drew above? The centre of the ellipse is the mid-point between the foci, namely (0,0).
anonymous
  • anonymous
ok
anonymous
  • anonymous
thanks
mathmate
  • mathmate
you're welcome! :)

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