an $x y$-equation and the $x y$-coordinates of a point $S$ are given. Find an $x^{\prime} y^{\prime}$-equation for the graph of the given equation if the origin of the $x^{\prime} y^{\prime}$-system is at the point $\mathbf{S}$.
$x^2+y^2-8 x+10 y-4=0 ; \mathbf{S}(4,-5)$