x2 – y2 – 2x + 2y = 0

Answer : 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 x2 – y2 – 2x + 2y = 0

Thus,

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

⇒ (X2 + 1 + 2X) – (Y2 + 1 + 2Y) – 2X – 2 + 2Y + 2 = 0

⇒ X2 + 1 + 2X – Y2 – 1 – 2Y – 2X + 2Y = 0

⇒ X2 – Y2 = 0

Hence, the transformed equation is X2 – Y2 = 0