Question 411504: analyze the equation x^2+9y^2+6x-18y+9=0; that is find the center,foci,vertices, and graph
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! analyze the equation x^2+9y^2+6x-18y+9=0; that is find the center,foci,vertices, and graph
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completing the squares,
(x^2+6x+9)+9(y^2-2y+1)=-9+9+9=9
(x+3)^2+9(y-1)^2=9
(x+3)^2/9+(y-1)^2/1=1
This equation is a standard form of an ellipse:(x-h)^2/a^2+(y-k)^2/b^2=1
Major axis is horizontal and center at (-3,1)
a^2=9
a=3
b^1=1
b=1
c=sqrt(a^2-b^2)=sqrt(8)=2.83
vertices: (-6,1) and 0,1)
foci: (4.83,1),(.83,1)
see graph below
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y=1+((9-(x+3)^2)/9)^.5
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