You can put this solution on YOUR website! graph x^2+9y^2+2x-18y+1=0
x^2+2x+9y^2-18y+1=0
(x^2+2x+1)+9(y^2-2y+1)=-1+1+9
(x+1)^2+9(y-1)^2=9
divide by 9
(x+1)^2/9+(y-1)^2=1
This is an equation of an ellipse with horizontal major axis and center at (-1,1)
see graph below:
y=±(1-((x+1)^2)/9)^.5+1