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Equation of an ellipse given c and eccentricity.

  1. Jan 27, 2013 #1
    1. The problem statement, all variables and given/known data
    Write the equation of the conic that meets the conditions:

    An ellipse that has the centre at (0, 0), has a horizontal major axis, the eccentricity is 1/2 and 2c = 1.


    2. Relevant equations

    [tex] \frac{(x - h)^2} {a^2} + \frac{(y - k)^2}{b^2} = 1 [/tex]



    3. The attempt at a solution

    2c = 1, [tex] c = \frac{1}{2} [/tex]

    e = c/a, so .5/1 = 1/2


    [tex] \frac{(x)^2} {1^2} + \frac{(y)^2}{b^2} = 1 [/tex]

    Not quite sure to go from here
     
  2. jcsd
  3. Jan 27, 2013 #2

    SteamKing

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    It's not clear what the parameter c is, but the eccentricity can also be defined in terms of a and b, the lengths of the semi-major and semi-minor axes.
     
  4. Jan 27, 2013 #3

    LCKurtz

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    Use ##a^2=b^2+c^2## for an ellipse.
     
  5. Jan 27, 2013 #4
    Since ## 2c = 1 ##, then ##c = .5 ##
    Making the variable ##a = 1##

    ##e = 1/2 = .5 / 1##

    ## (1)^2 = b^2 + (.5)^2 ##
    ## 1 - .25 = b^2 ##
    ## b^2 = 3/4 ##

    So this would set the answer to:

    ## x^2 + \frac{3(y^2)}{4} = 1 ##

    Correct?
     
  6. Jan 27, 2013 #5

    LCKurtz

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    Check your ##\frac{y^2}{b^2}##.
     
  7. Jan 27, 2013 #6
    Oops

    ## x^2 + \frac{4(y^2)}{3} = 1 ##


    Thanks a million :)
     
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