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Math Help - Ellipse

  1. #1
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    Ellipse

    Q: The ellipse D has equation \frac{x^2}{25} + \frac{y^2}{9} = 1 and the ellipse E has equation \frac{x^2}{4} + \frac{y^2}{9} =1. The point S is a focus of D and the point T is a focus of E. Find the length of ST.
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    As the major axis for ellipse E is the y-axis, does that mean that the focus lies on that axis too? Also, can someone draw a picture showing me what it is asking for? Thanks in advance.
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  2. #2
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    I'm assuming you know some basics about ellipses in this solution:

    For ellipse D: \frac{x^2}{25} + \frac{y^2}{9} = 1
    An important equation for ellipses:  b^2 = a^2 (1-e^2) where a = 5, b =3, e = eccentricity
    e = \frac{4}{5}
    Focus S is  (\pm ae,0) = (\pm 4,0)

    For ellipse E:  \frac{x^2}{4} + \frac{y^2}{9} =1
    Because b is larger than a, the major axis, where the focus lies, is the y axis.
     a^2 = b^2(1-e^2) where a = 2, b = 3
     e = \frac{\sqrt5}{3}
    Focus T is  (0,\pm be) = (0,\pm \sqrt5)

    Now use the distance formula to find the distance between ST. Since there are two focus for each ellipse, I imagine you need to find the distance between each of them, but I'm pretty sure they will all be the same distance.
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