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

Question

Find what the given equation becomes when the origin is shifted to the point (1, 1). x 2 – y 2 – 2x + 2y = 0

Philoid · Accepted 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