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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