A square is inscribed in the circle $x^2+y^2-2x-4y+\lambda =0$ whose sides are parallel to coordinate axes then vertices of square are 
 

$$\begin{gathered} {\mathrm{x}}^2+{\mathrm{y}}^2-4\mathrm{x}+6\mathrm{y}-5=0 \\ \mathrm{centre}=(2, -3) \\ \mathrm{r}=\sqrt{4+9+5}=3\sqrt{2} \\ vertices of square are (x_1\pm r\cos \theta ,y_1\pm r\sin \theta ) \\ =\left(2\pm 3\sqrt{2}.\frac{1}{\sqrt{2}}, -3\pm 3\sqrt{2}.\frac{1}{\sqrt{2}}\right) \\ =(2\pm 3, -3\pm 3) \\ \therefore vertices are (5, 0), (-1, -6) ,(5, -6) ,(-1, 0) \end{gathered}$$