Find what the given equation becomes when the origin is shifted to the point (1, 1).

xy – y2 – x + y = 0


Let the new origin be (h, k) = (1, 1)

Then, the transformation formula become:


x = X + 1 and y = Y + 1


Substituting the value of x and y in the given equation, we get


xy – y2 – x + y = 0


Thus,


(X + 1)(Y + 1) – (Y + 1)2 – (X + 1) + (Y + 1) = 0


XY + X + Y + 1 – (Y2 + 1 + 2Y) – X – 1 + Y + 1 = 0


XY + X + Y + 1 – Y2 – 1 – 2Y – X + Y = 0


XY – Y2 = 0


Hence, the transformed equation is XY – Y2 = 0


1