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

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

$x y-y^{2}-x+y=0$

Thus

$(X+1)(Y+1)-(Y+1)^{2}-(X+1)+(Y+1)=0$

$\Rightarrow X Y+X+Y+1-\left(Y^{2}+1+2 Y\right)-X-1+Y+1=0$

$\Rightarrow X Y+X+Y+1-Y^{2}-1-2 Y-X+Y=0$

$\Rightarrow X Y-Y^{2}=0$

Hence, the transformed equation is $X Y-Y^{2}=0$