anonymous
  • anonymous
PLEASE HELP ME WRITE THE EQUATION FOR AN ELLIPSE: (MEDAL AND FAN!!!): Write the equation of an ellipse with center (2,1); vertex (7,1) ; and focus (5,1).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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ganeshie8
  • ganeshie8
|dw:1439810883867:dw|
anonymous
  • anonymous
Ok that makes sense, so how do I get a? I am just confused sorry.
ganeshie8
  • ganeshie8
|dw:1439810946525:dw|

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More answers

ganeshie8
  • ganeshie8
so it seems it is going to be a horizontal ellipse ?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
I know that the equation is going to look like this: \[\frac{ (x-2)^2 }{ ? } + \frac{ (y-1)^2 }{ ? } = 1\]
ganeshie8
  • ganeshie8
Right, center = \((h,k)=(2,1)\) we need to find the values of \(a,b\) and plug in : \[\dfrac{(x-2)^2}{a^2}+\dfrac{(y-1)^2}{b^2}=1\]
anonymous
  • anonymous
I just need a^2 and b^2...
ganeshie8
  • ganeshie8
use the vertex formula : \((h+a, k)=(7,1)\) can you find the value of \(a\) ?
anonymous
  • anonymous
is it 5?
ganeshie8
  • ganeshie8
Correct. \(2+a=7\implies a=5\)
anonymous
  • anonymous
ok and then b?
ganeshie8
  • ganeshie8
Next use focus formula \((h+c,~k)=(5,1)\) can you find the value of \(c\) ?
anonymous
  • anonymous
Is it 2?
ganeshie8
  • ganeshie8
nope
anonymous
  • anonymous
Not sure, sorry
ganeshie8
  • ganeshie8
\(h+c=5\) you know that \(h=2\), therefore \(c=?\)
anonymous
  • anonymous
3?
ganeshie8
  • ganeshie8
Yes, \(a=5,~c=3\) we still need to find \(b\)
anonymous
  • anonymous
ok so I use this right: c^2 = b^2 - a^2?
ganeshie8
  • ganeshie8
it should be \(a^2 = b^2+c^2\)
anonymous
  • anonymous
whoops ok, sorry: 5^2 = 3^2 + b^2 25 = 9 + b^2 16 = b^2 b = 4
ganeshie8
  • ganeshie8
Excellent!
anonymous
  • anonymous
Ok so my final answer is: \[\frac{ (x-2)^2}{ 25 } + \frac{ (y-2)^2 }{ }\]
anonymous
  • anonymous
whoops i messed that up under the (y-2)^2 is 16. and it all equals 1 right?
anonymous
  • anonymous
Ok so now that i got that, how do I approach this when I am given center, co-vertex, and focus? Can i post the question?
ganeshie8
  • ganeshie8
Ok so my final answer is: \[\frac{ (x-2)^2}{ 25 } + \frac{ (y-\color{red}{1})^2 }{ \color{red}{16} }\]
anonymous
  • anonymous
Sorry that is what i meant, lol i had that written down...

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