Ms Sue Please Help ! Analytic Geometry

Identify the points and graph the equation of the ellipse. 9x^2 + 4y^2 -54x-16y + 61 =0

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  1. what do you mean "identify the points"?

    9x^2 + 4y^2 -54x-16y + 61 =0
    9x^2-54x + 4y^2-16y = -61
    9(x^2-6x) + 4(y^2-4y) = -61
    9(x^2-6x+9) + 4(y^2-4y+4) = -61 + 9*9 + 4*4
    9(x-3)^2 + 4(y-2)^2 = 36

    (x-3)^2/4 + (y-2)^2/9 = 1

    ellipse with major axis vertical, semi-axes of length 2 and 3.
    Center at (3,2)
    Foci at (3,2±√5)
    e = √5/3

    http://www.wolframalpha.com/input/?i=foci+of+9x^2+%2B+4y^2+-54x-16y+%2B+61+%3D0+

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    posted by Steve

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