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anonymous

  • one year ago

Find the equation of an ellipse with vertices (3, 0) and (-3, 0) and foci of (2, 0) and (-2, 0). I dont know which formula to use!!! Please help me out?

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  1. anonymous
    • one year ago
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    I know the answer to this question, its given in my textbook, but Im so confused on when to use which formula: The Major Axis Horizontal Formula? \[\frac{ x ^{2} }{ a ^{2} }+\frac{ y ^{2} }{ b ^{2} }\] Or the Major Axis Vertical Formula? \[\frac{ x ^{2} }{ b ^{2} }+\frac{ y ^{2} }{ a ^{2} }\]

  2. Jhannybean
    • one year ago
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    First off, let's graph it.|dw:1439370727299:dw|

  3. Jhannybean
    • one year ago
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    From our formula for an ellipse, \(\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}\) we find that our center lies at \((0,0)\), therefore our equation turns into: \[\frac{x^2}{a^2}+\frac{y^2}{b^2}\]

  4. anonymous
    • one year ago
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    And if our center is greater than zero, we use the other formula?

  5. Jhannybean
    • one year ago
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    Secondly, just by graphing it, and looking at where our focus and vertices lie, we know that our ellipse is stretching horizontally, therefore \(a^2\) corresponds with \(x\) and \(b^2\) corresponds with \(y\)

  6. Jhannybean
    • one year ago
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    We can now use the formula \(c^2=a^2+b^2\) to find our value of b.

  7. Jhannybean
    • one year ago
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    We have our value of \(a\), and that is the distance from the center to one of the vertices along the `major` axis. Therefore, \(a=3\)|dw:1439371651892:dw|

  8. Jhannybean
    • one year ago
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    \(c\) is our distance from the center to one of the two foci. Therefore \(c=2\)|dw:1439371729613:dw|

  9. Jhannybean
    • one year ago
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    using the pythagorean theorem, be can find \(b\). \[c^2=a^2+b^2 \iff b^2=c^2-a^2\]

  10. Jhannybean
    • one year ago
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    Do you see it now? With the given information, do you understand why I chose the formula I chose and how to input the information to find your equation?

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