Without change of axes the origin is shifted to (h, k), then from the equation $x^2 + y^2 – 4x + 6y – 7 = 0$ the terms containing linear powers are missing. The points (h, k) is

$$\begin{gathered} Given equation x^2+y^2-4x+6y-7=0 \\ when origin is shifted to the point (h,k) \\ the above equation is transformed to \\ X^2+Y^2+(2h-4)X+(2k+6)Y+h^2+k^2-4h+6k-7=0 \\ To ,eliminate linear terms we should have 2h-4=0 and 2k+6=0 \\ \Rightarrow h=2 and k=-3 \\ \therefore (h,k)=(2,-3) \end{gathered}$$