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Conic Sections - Ellipses

  1. Nov 12, 2007 #1
    1. The problem statement, all variables and given/known data
    Center is at (4, -1)
    Vertex is at (4, -5)
    Focus is at (4, -3.5)

    Find the equation of the ellipse.

    2. Relevant equations
    horizontal ellipse: ((x-h)^2)/(a^2)) + ((y-k)^2)/(b^2)) = 1
    Vertical ellipse: ((y-k)^2)/(a^2)) + ((x-h)^2)/(b^2)) = 1
    c^2 = a^2 - b^2

    3. The attempt at a solution
    The distance between the vertex and the center is 4, so a = 4.

    Based on the focus, I got:

    -3.5 = 1 + c
    c = -2.5

    then I did c^2 = a^2 - b^2
    to get 6.25 = 16 - b^2
    b^2 = 9.75

    I put in a^2 (16) and b^2 (9.75) into the equation
    Vertical ellipse: ((y-k)^2)/(a^2)) + ((x-h)^2)/(b^2)) = 1
    to get: ((y+1)^2)/16) + ((x-4)^2)/9.75) = 1

    However, the correct answer is: (4(x-4)^2)/39) + (((y+1)^2)/16). I can't seem to figure out how to arrive at the correct answer. Help is greatly appreciated.
     
  2. jcsd
  3. Nov 12, 2007 #2

    Dick

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    Science Advisor
    Homework Helper

    4/39=1/9.75.
     
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