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