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Precalc

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An ellipse has this Cartesian equation:
((x-2)/5)^2 + ((y-4)/3)^2 = 1

Find the focal radius

Find the eccentricity

Write the parametric equations for the ellipse

Transform into the form, Ax^2 + By^2 + Cx + Dy + E = 0

  • Precalc -

    I don't know which author you use, but focal radius can be defined in more than one way
    http://www.mathwords.com/f/focal_radius.htm

    for yours,
    a = 5, b = 3
    your ellipse will be horizontal, and
    b^2 + c^2 = a^2
    9+c^2 = 25
    c^2 = 16
    c = 4

    eccentricity = c/a = 4/5 = .8

    parametric equations:
    x-2 = 5coss t ---> x = 5cost + 2
    y-4 = 3sin t ----> y = 3sint + 4

    original:


    (x-2)^2 /25 + (y-4)^2 / 9 = 1
    multiply by 225
    9(x-2)^2 + 25(y-4)^2 = 225
    9(x^2 - 4x + 4) + 25(y^2 - 8y + 16) = 225
    I am sure you can finish it.

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