Lilmike234
  • Lilmike234
What is the equation of an ellipse centered at (5,-1) having a horizontal minor axis of length 4 and a major axis of length 6?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
do you know the general form of an ellipse with center \((h,k)\)?
anonymous
  • anonymous
just asking is all if the answer is "NO" i will show you
Lilmike234
  • Lilmike234
No I don't

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anonymous
  • anonymous
no one likes these conic section problems but they are not that hard
anonymous
  • anonymous
general form of ellipse with center \((h,k)\) is \[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\] you are already given \((h,k)\) all you need now is \(a\) and \(b\)
Lilmike234
  • Lilmike234
(x-5)^2/36+(y-1)^2/16=1 was the equation I got is this correct ?
anonymous
  • anonymous
could be let me check
anonymous
  • anonymous
no but you have the right idea
Lilmike234
  • Lilmike234
Or was is suppose to be (x+5)^2/9+(y+1)^2/4=1 ?
anonymous
  • anonymous
first off "horizontal minor axis" is shorter than the "vertical major axis" that means it looks like this |dw:1439255560209:dw|
anonymous
  • anonymous
second answer is even closer, you got the deominators right, but they are backwards
anonymous
  • anonymous
half of 6 is 3 and \(3^2=9\) likewise \(2^2=4\) but since it is oriented the other way, the larger number should be under the \(y\) term not the x terms
Lilmike234
  • Lilmike234
So (x-5)^2/9+(y-1)^2/4=1?
anonymous
  • anonymous
looks like this http://www.wolframalpha.com/input/?i=ellipse+%28x-5%29^2%2F4%2B%28y%2B1%29^2%2F9%3D1
anonymous
  • anonymous
again the larger number should be under the \(y\) term since the major axis is vertical
anonymous
  • anonymous
\[\frac{(x-5)^2}{4}+\frac{(y+1)^2}{9}=1\]

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