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anonymous

  • one year ago

What is the equation of the ellipse with co-vertices (0, 2), (0, -2) and vertices (3, 0), (-3, 0)? Please help? I have nO IDEA how to do this!

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  1. UnkleRhaukus
    • one year ago
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    hmmm, lets draw a graph, and plot those points

  2. UnkleRhaukus
    • one year ago
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    |dw:1439094439604:dw|

  3. UnkleRhaukus
    • one year ago
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    |dw:1439094488079:dw| can you do the others?

  4. UnkleRhaukus
    • one year ago
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    (click on the yellow pencil icon, to reuse a drawing )

  5. anonymous
    • one year ago
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    |dw:1439094586269:dw| is this correct?

  6. UnkleRhaukus
    • one year ago
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    whoops, i plotted that first point wrong,

  7. UnkleRhaukus
    • one year ago
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    (my mistake) |dw:1439094795562:dw|

  8. UnkleRhaukus
    • one year ago
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    [that's better now (sorry about that)] now we have the co-vertices plotted, we can draw the ellipse , so that is goes through these points . . .

  9. UnkleRhaukus
    • one year ago
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    (can you draw the ellipse?)

  10. anonymous
    • one year ago
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    |dw:1439094980170:dw|

  11. UnkleRhaukus
    • one year ago
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    Good. |dw:1439095016485:dw|

  12. UnkleRhaukus
    • one year ago
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    Can you tell from the diagram now, where the centre of ellipse is ? and its semi-major axes?

  13. anonymous
    • one year ago
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    (0,0)

  14. UnkleRhaukus
    • one year ago
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    good, yes that is the centre

  15. UnkleRhaukus
    • one year ago
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    And remember that the axes are half the width (a), and half the height (b)

  16. anonymous
    • one year ago
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    it's 6, and 4, right?

  17. UnkleRhaukus
    • one year ago
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    the major axes (full width/height) are 6 and 4 we want the semi-major axes ... half these

  18. anonymous
    • one year ago
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    3, and 2

  19. UnkleRhaukus
    • one year ago
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    you now have \((h,k)=(0,0)\) \(a=3\), \(b =2\) so plug these into \[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1\]

  20. UnkleRhaukus
    • one year ago
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    What do you get:

  21. anonymous
    • one year ago
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    (|dw:1439095772471:dw|

  22. UnkleRhaukus
    • one year ago
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    very good, now just simplify

  23. anonymous
    • one year ago
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    |dw:1439095814555:dw|

  24. anonymous
    • one year ago
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    y^2

  25. UnkleRhaukus
    • one year ago
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    |dw:1439095846244:dw|

  26. UnkleRhaukus
    • one year ago
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    Great work! you're done

  27. anonymous
    • one year ago
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    Thank you once again! :)

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