Question:
Find what the given equation becomes when the origin is shifted to the point (1, 1).
$x y-x-y+1=0$
Solution:
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
$x y-x-y+1=0$
Thus,
$(X+1)(Y+1)-(X+1)-(Y+1)+1=0$
$\Rightarrow X Y+X+Y+1-X-1-Y-1+1=0$
$\Rightarrow X Y=0$
Hence, the transformed equation is XY = 0
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