Ellipse

Let $u = x + y$ and $v = x - y$ , then the given equation becomes:

$\dfrac{ (u - 2)^2 }{3^2} + \dfrac{v^2}{4} = 1$

Which is an ellipse in the (u, v) reference frame with center $(u, v) = (2, 0)$ . Solving for (x, y) in terms of (u, v), we obtain,

$(x, y) = ( \dfrac{ u + v }{2} , \dfrac{ u - v } {2} )$

Hence, in the (x, y) reference frame, the center is given by:

$(x, y) = ( \dfrac{ 2 + 0 }{2} , \dfrac{ 2 - 0 } {2} ) = (1, 1)$