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Question
Find what the following equation become when the origin is shifted to the point (1, 1).
x2 − y2 − 2x + 2y = 0
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Solution
The given equation is x2 − y2 − 2x + 2y = 0.
Substituting \[x = X + 1, y = Y + 1\] in the given equation, we get:
\[\left( X + 1 \right)^2 - \left( Y + 1 \right)^2 - 2\left( X + 1 \right) + 2\left( Y + 1 \right) = 0\]
\[ \Rightarrow X^2 + 2X + 1 - Y^2 - 2Y - 1 - 2X - 2 + 2Y + 2 = 0\]
\[ \Rightarrow X^2 - Y^2 = 0\]
Hence, the transformed equation is \[x^2 - y^2 = 0\]
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