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Math Help - Need help finding foci of an ellipse

  1. #1
    Newbie JoanneMac's Avatar
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    Exclamation Need help finding foci of an ellipse

    of this equation: x^2/25+y^2/36=1

    I know the x-intercepts are (5, -5) and the y-intercepts are (6, -6), but don't know how to find the foci.

    Please help!

    You can answer me right here because I check often enough.
    Joanne
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  2. #2
    MHF Contributor
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    Hello

    Your equation is x/a + y/b = 1 with a = 5 and b = 6
    Have a look to the picture above but exchanging a and b since a < b (or rotate the ellipse of 90)
    c = b - a = 11
    Foci are therefore placed at (0, sqrt(11)) and (0,-sqrt(11))

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  3. #3
    Senior Member vincisonfire's Avatar
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    The definition of an ellipse a line. The sum of the distance to each foci of each point is the same.
    You know because of the y-intercept that this is equal to
     (6+y)+(6-y) = 12
    Then from the x-intercept you know that  12 = 2\sqrt{5^2+y^2}
     y =\pm \sqrt(11)
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