Find what the given equation becomes when the origin is shifted to the point (1, 1).
xy – x – y + 1 = 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 – x – y + 1 = 0
Thus,
(X + 1)(Y + 1) – (X + 1) – (Y + 1) + 1 = 0
⇒ XY + X + Y + 1 – X – 1 – Y – 1 + 1 = 0
⇒ XY = 0
Hence, the transformed equation is XY = 0