Find what the given equation becomes when the origin is shifted to the point

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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