SOLUTION: Determine if the given equation describes ellipse, or hyperbola. Also write each in standard form. x^2+9y^2-8x-90y+232=0

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Question 703148: Determine if the given equation describes ellipse, or hyperbola. Also write each in standard form.
x^2+9y^2-8x-90y+232=0
Answer by lwsshak3(11628) About Me  (Show Source):
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Determine if the given equation describes ellipse, or hyperbola. Also write each in standard form.
x^2+9y^2-8x-90y+232=0
x^2-8x+9y^2-90y+232=0
x^2-8x+9y^2-90y=-232
complete the squares
(x^2-8x+16)+9(y^2-10y+25)=-232+16+225
(x-4)^2+9(y-5)^2=9
%28x-4%29%5E2%2F9%2B%28y-5%29%5E2=1
This is an equation of an ellipse with horizontal major axis and center at (4,5)
Its standard form: %28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1, a>b, (h,k)=(x,y) coordinates of center