Q. 85.0( 1 Vote )

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

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


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