By translation of axes the equation xy – x + 2y – 6 = 0 changed as xy = c then c =

$$\begin{gathered} \mathrm{Given} \mathrm{equation} \mathrm{xy}-\mathrm{x}+2\mathrm{y}-6=0 \\ \Rightarrow \mathrm{xy}-\mathrm{x}+2\mathrm{y}-2-4=0 \\ \Rightarrow \mathrm{x}(\mathrm{y}-1)+2(\mathrm{y}-1)=4 \\ \Rightarrow (\mathrm{y}-1)(\mathrm{x}+2)=4 \\ \Rightarrow (\mathrm{x}+2)(\mathrm{y}-1)=4 \\ If origin is shifted to the point (-2,1) it is reduced to the form XY=4 \\ Compare with \mathrm{XY}=c \\ \therefore c=4 \end{gathered}$$