Question

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

x² + xy – 3x – y + 2 = 0

Answer 1

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 + xy – 3x – y + 2 = 0

Thus,

(X + 1)² + (X + 1)(Y + 1) – 3(X + 1) – (Y + 1) + 2 = 0

⇒ (X² + 1 + 2X) + XY + X + Y + 1 – 3X – 3 – Y – 1 + 2 = 0

⇒ X² + 1 + 2X + XY – 2X – 1 = 0

⇒ X² + XY = 0

Hence, the transformed equation is X² + XY = 0