The centre of the ellipse (x+y−2)216+(x−y)29=1 is:

The equation of the ellipse is 9(x+y−2)2+16(x−y)2=144→(1) Differentiating (1) with respect to x, treating y as constant , we get , 18(x+y−2)+32(x−y)=0→(2) Differentiating (1) with respect to y, treating x as constant , we get ,18(x+y−2)−32(x−y)=0→(3) Solving (2) and (3), we get the coordinates of the centre (1, 1).