Write the equation of an ellipse centered at the origin with foci at (0, -3) and (0, 3) and a major axis of 10.?

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  • DWRead
    Lv 7
    6 months ago
    Best Answer

    The foci are vertically aligned (they have the same x-coordinates), so the ellipse is vertical.

    General equation for a vertical ellipse:

     (y-k)²/a² + (x-h)²/b² = 1

    with

     a² ≥ b²

     center (h,k)

     vertices (h,k±a)

     length of major axis = 2a

     co-vertices (h±b,k)

     foci (h,k±c), c² = a²-b²

    Apply your given information and solve for h, k, a, and b.

    center (h,k) = (0,0)

    h = k = 0

    length of major axis = 2a = 10

    a = 5

    foci (h,k±c) = (0,0±3)

    c = 3

    b² = a² - c² = 16

    b = 4

    The equation becomes

     y²/25 + x²/16 = 1

    Attachment image
  • 6 months ago

    (x/4)^2+(y/5)^2=1

    =>

    (x^2)/16+(y^2)/25=1

  • 6 months ago

    (x/√((10/2)² - 3²))² + (y/3)² = 1

    (x/4)² + (y/3)² = 1

  • 6 months ago

    The major axis lies along the y-axis, and the minor axis lies along the x-axis (because the foci are on the y-axis). The semi-minor axis is sqrt(a^2 - c^2) = 4.

    x^2/16 + y^2/9 = 1.

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