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anonymous

  • one year ago

What is the equation of the following graph?

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  1. anonymous
    • one year ago
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  2. UnkleRhaukus
    • one year ago
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    looks like an ellipse, where is it centred? what are the semimajor axes?

  3. anonymous
    • one year ago
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    it is, and isn't it centered at (0,0)? and I don't know them..

  4. UnkleRhaukus
    • one year ago
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    yes it is centred at the origin: (0,0)

  5. UnkleRhaukus
    • one year ago
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    Semi major axes of an ellipse look like this |dw:1439092799738:dw|

  6. anonymous
    • one year ago
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    |dw:1439092817312:dw| we have to use this equation, correct?

  7. UnkleRhaukus
    • one year ago
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    A general form of an ellipse centred at the point \((h,k)\), with semi major axes \(a\), and \(b\), (in the x and y directions respectively ) is \[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1\]

  8. UnkleRhaukus
    • one year ago
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    yeah we have the centre \((h,k)\) = \((0,0)\) so it reduces to \[\frac{x^2}{a^2}+\frac{y^2}{b^2} = 1\]

  9. UnkleRhaukus
    • one year ago
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    we just need to get \(a\), (half the width) and \(b\), (half the height)

  10. anonymous
    • one year ago
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    how do we get that?

  11. UnkleRhaukus
    • one year ago
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    look at the diagram,

  12. UnkleRhaukus
    • one year ago
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    |dw:1439093170591:dw|

  13. anonymous
    • one year ago
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    so then A would be 1.5, and B would be 3 ?

  14. UnkleRhaukus
    • one year ago
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    not quite, the full width of the ellipse is 3 - (-3) = 6 the full height of the ellipse is 6 - (-6) = 12 so half the width is 6/2 = ... and the half height is 12/2 = ......

  15. anonymous
    • one year ago
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    3, and 6, or is it in that fraction form?

  16. UnkleRhaukus
    • one year ago
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    thats right the semi-major axis (in the x direction) : a = 3 and the semi-major axis in the y direction: b = 6

  17. UnkleRhaukus
    • one year ago
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    So what does the equation of our ellipse look like now?

  18. anonymous
    • one year ago
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    |dw:1439093577574:dw|

  19. UnkleRhaukus
    • one year ago
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    goood, now just simplify 3^2 and simplify 6^2

  20. anonymous
    • one year ago
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    9 & 36

  21. UnkleRhaukus
    • one year ago
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    Cool, so your equation is \[\frac{x^2}9+\frac{y^2}{36} = 1\] A further step to make the final equation a little nicer could be to multiply both sides by 9 \[x^2+\frac{y^2}{4} = 9\] but you might prefer to keep it as \(\frac{x^2}9+\frac{y^2}{36} = 1\)

  22. anonymous
    • one year ago
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    Thank you! :)

  23. UnkleRhaukus
    • one year ago
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    i suppose another option for a nice final form might be \[\left(\frac x3\right)^2+\left(\frac y6\right)^2=1\] They all kinda look nice.

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