Step 1:

$xy-kx-hy=0$

The combined equation of the asymptotes differs only in the constant term.

Now $xy-kx-hy=xy-kx-hy+kh-kh$

$\Rightarrow x(y-k)-h(y-k)-kh$

$\Rightarrow (x-h)(y-k)-kh$

Therefore the equation of the rectangular hyperbola is $(x-h)(y-k)-kh=0$

$(x-h)(y-k)=kh$

Step 2:

This is of the form $(x-h)(y-k)=c^2$ and is an rectangular hyperbola with centre $(h,k)$ and asymptotes $x-h=0,y-k=0$