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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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    @Michele_Laino

  2. Michele_Laino
    • one year ago
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    that is a traslated ellipse

  3. Michele_Laino
    • one year ago
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    as you can see from the graph, the center of our ellipse is located at (0,-2)

  4. anonymous
    • one year ago
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    y2/9+x2/1

  5. Michele_Laino
    • one year ago
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    no, since we have to make a traslation

  6. Michele_Laino
    • one year ago
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    let's consider a new coordinate system X,Y located at point (0,2), namely at the center of your ellipse

  7. Michele_Laino
    • one year ago
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    with respect to the XY system the equation of our ellipse is: \[\Large \frac{{{X^2}}}{1} + \frac{{{Y^2}}}{9} = 1\]

  8. Michele_Laino
    • one year ago
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    am I right?

  9. anonymous
    • one year ago
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    yes

  10. Michele_Laino
    • one year ago
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    here is the situation of your exercise: |dw:1439652920237:dw|

  11. Michele_Laino
    • one year ago
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    oops.. I made a typo, the center of our ellipse is located at poin (0,-2)

  12. Michele_Laino
    • one year ago
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    and the equations of our traslation are: \[\Large \left\{ \begin{gathered} x = X \hfill \\ y = Y - 2 \hfill \\ \end{gathered} \right.\]

  13. anonymous
    • one year ago
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    okay

  14. Michele_Laino
    • one year ago
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    now, please solve that system for X, and Y, what do you get?

  15. anonymous
    • one year ago
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    im lost now.

  16. Michele_Laino
    • one year ago
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    hint: we have this: \[\Large X = x\] right?

  17. anonymous
    • one year ago
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    yes

  18. sohailiftikhar
    • one year ago
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    what you want to know?

  19. Michele_Laino
    • one year ago
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    ok! now do the same, namely write Y as a function of y, please

  20. anonymous
    • one year ago
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    y=y-2 ?

  21. Michele_Laino
    • one year ago
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    \[\Large Y = y + 2\]

  22. anonymous
    • one year ago
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    oh okay

  23. Michele_Laino
    • one year ago
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    next, replace X with x, and Y with y+2 into my equation above

  24. Michele_Laino
    • one year ago
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    namely into this equation: \[\Large \frac{{{X^2}}}{1} + \frac{{{Y^2}}}{9} = 1\] what equation do you get?

  25. anonymous
    • one year ago
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    idk im lost again..im glad im going over this other wise i would have gotten this wrong

  26. Michele_Laino
    • one year ago
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    hint: \[\Large \frac{{{x^2}}}{1} + \frac{{{{\left( {y + 2} \right)}^2}}}{9} = 1\] is it right?

  27. anonymous
    • one year ago
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    yes

  28. Michele_Laino
    • one year ago
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    that is the requested equation

  29. anonymous
    • one year ago
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    so that the anwser?

  30. Michele_Laino
    • one year ago
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    yes!

  31. Loser66
    • one year ago
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    For shifted one, you need center (h, k), the way to find out a, b as what we had done before. The way a goes with major axis is the same. Just the numerators change to (x-h) ^2 and (y-k)^2. Dat sit.

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