Ok so i have this conic : x^2 - 4xy + y^2 - 6x -12y + 8 = 0

The problem asks to reduce it to it's canonical form and represent it graphically so i reached:

X=x`+3*sqrt2 and Y = y` -3*sqrt2 from this : -1(x`+3sqrt2)^2 + 3(y` -3*sqrt2)^2 - 28 = 0 but i'm a bit unclear on how the final form should be and how to represent it graphically i mean i know e1 = (1/sqrt2 , 1/sqrt2) and e2 = (-1/sqrt2 , 1/sqrt2) with those i can draw the new axis but because i em not sure about how the final form of this -1(x`+3sqrt2)^2 + 3(y` -3*sqrt2)^2 - 28 = 0 should be idk how to draw it, a full draw step by step would help a lot.