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

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

Thus,

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

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

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

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

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