Answer :

Let the new origin be (h, k) = (1, -2) Then, the transformation formula become:

x = X + 1 and y = Y + (-2) = Y – 2

Substituting the value of x and y in the given equation, we get 2×2 + y2 – 4x + 4y = 0

Thus,

2(X + 1)2 + (Y – 2)2 – 4(X + 1) + 4(Y – 2) = 0

⇒ 2(X2 + 1 + 2X) + (Y2 + 4 – 4Y) – 4X – 4 + 4Y – 8 = 0

⇒ 2X2 + 2 + 4X + Y2 + 4 – 4Y – 4X + 4Y – 12 = 0

⇒ 2X2 + Y2 – 6 = 0

⇒ 2X2 + Y2 = 6

Hence, the transformed equation is 2X2 + Y2 = 6