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