anonymous
  • anonymous
find a set of parametric equations for the line or conic. Ellipse: Vertices: (+/-5,0) & Foci: (+/-4,0)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
do you know what the center is?
anonymous
  • anonymous
|dw:1377653475866:dw|
anonymous
  • anonymous
no it provides us with that

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anonymous
  • anonymous
the center of the ellipse is the two foci isn't it?
anonymous
  • anonymous
right i know, my question really meant "given the information, what is the center?"
anonymous
  • anonymous
no there is one center for an ellipse two foci, but one center it is half way between the foci, so in this case it is right at the origin \((0,0)\)
anonymous
  • anonymous
the general form of an ellipse is \[\frac{(x-h)^2}{a^2}+\frac{(y-h)^2}{b^2}=1\] but in your example, since the center is \((0,0)\) it is \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\] and your job now is to find \(a\) and \(b\)
anonymous
  • anonymous
there asking for two parametric equations and would would put them into these x-h+acos theta y=k+bcos theta i just don't know what to plug in where
anonymous
  • anonymous
oh i see you can ignore the \(h\)and \(k\) part because the center is \((0,0)\) and so \(h=k=0\)
anonymous
  • anonymous
so it is just going to be \[x=a\cos(\theta)\] and \[y=b\sin(\theta)\]
anonymous
  • anonymous
since the ellipse travels through the point \((5,0)\) you know it is \[x=5\cos(\theta)\]
anonymous
  • anonymous
does the negative have any influence?
anonymous
  • anonymous
that way when \(\theta=0\) you get \(5\cos(0)=5\) and \(5\sin(0)=0\)
anonymous
  • anonymous
no not really \(\theta\) will go form \(0\) to \(2\pi\) so you will get negative values that way the only work you need to do here is to find where the ellipse hits the \(y\) axis so you can put that number for \(b\) in \(b\sin(\theta)\)
anonymous
  • anonymous
and you do that by noting that \(a^2=b^2+c^2\) or in your case \[5^2=b^2+4^2\] making \[b=3\]
anonymous
  • anonymous
your parametric equations are therefore \[x=5\cos(\theta), y=3\sin(\theta)\]
anonymous
  • anonymous
and the 4 means basically nothing?
anonymous
  • anonymous
oh no it means something it tells you what the foci are but in this case it tells you how to find \(b\)
anonymous
  • anonymous
ok. thanks!!!!
anonymous
  • anonymous
yw
anonymous
  • anonymous
how would you solve this type of problem but for a hyperbola?

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