# Math Help - ellipse, center, axis

1. ## ellipse, center, axis

Hi there,

I am a little rusty with geometry.. I have this ellipse:

f(x,y)=(x-1)^2+(x-1)(y-1)+(y-1)^2-3*(x+y-2)=0

I drew the graph with the help of a software and observed that is tangent to (0,3) and (3,0). It is a tilded ellipse. Can anyone tell me what is the center and what are the four pairs of points (on the perimeter of the ellipse) that construct the major and the minor axis? Also can anyone provide the general formula of an ellipse whos center is not (0,0) and is also tilted. I am a little lost..

2. There are several ways to do it, but I don't what have you covered. For example for a ellipse $f(x,y)=0$ (in general for any conic) its center satisfies $f_x=0,f_y=0$.