Q. 85.0( 1 Vote )

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

x^{2} – y^{2} – 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

x^{2} – y^{2} – 2x + 2y = 0

Thus,

(X + 1)^{2} – (Y + 1)^{2} – 2(X + 1) + 2(Y + 1) = 0

⇒ (X^{2} + 1 + 2X) – (Y^{2} + 1 + 2Y) – 2X – 2 + 2Y + 2 = 0

⇒ X^{2} + 1 + 2X – Y^{2} – 1 – 2Y – 2X + 2Y = 0

⇒ X^{2} – Y^{2} = 0

Hence, the transformed equation is X^{2} – Y^{2} = 0

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

xy – x – y + 1 = 0

RS Aggarwal - Mathematics

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

x^{2} – y^{2} – 2x + 2y = 0

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