X 2+y 2-2x+4y = 0。 What is the maximum value of X-2Y? X 2+y 2-2x+4y = (x-1) 2+(y+2) 2 = 5 can be regarded as a circle, so x-2y=k can be regarded as a straight line, and the straight line intersects or is tangent to the circle. As can be seen from the figure, the tangency in the upper left direction is the smallest, and the tangency in the lower right direction is the largest. ...