The sides
![\[\begin{array}{*{35}{l}} x\text{ }-\text{ }3y\text{ }=\text{ }4\text{ }\ldots .\text{ }\left( 1 \right) \\ 3x\text{ }+\text{ }y\text{ }=\text{ }22\text{ }\ldots \text{ }\left( 2 \right) \\ x\text{ }-\text{ }3y\text{ }=\text{ }14\text{ }\ldots .\text{ }\left( 3 \right) \\ 3x\text{ }+\text{ }y\text{ }=\text{ }62\text{ }\ldots \text{ }\left( 4 \right) \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8ce1891b0c15174c3f272365578c698c_l3.png "Rendered by QuickLaTeX.com")
assuming A, B, C, D as the vertices of the square and solving the lines, we get :
A = (7, 1)
B = (8, – 2)
C = (20, 2)
D = (19, 5)
the equation of the circle with diagonal AC as diameter is given by
![\[\begin{array}{*{35}{l}} (x\text{ }-\text{ }{{x}_{1}})\text{ }(x\text{ }-\text{ }{{x}_{2}})\text{ }+\text{ }(y\text{ }-\text{ }{{y}_{1}})\text{ }(y\text{ }-\text{ }{{y}_{2}})\text{ }=\text{ }0 \\ \left( x\text{ }-\text{ }7 \right)\text{ }\left( x\text{ }-\text{ }20 \right)\text{ }+\text{ }\left( y\text{ }-\text{ }1 \right)\text{ }\left( y\text{ }-\text{ }2 \right)\text{ }=\text{ }0 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b33644a807ab298fdfbc67c3ba53a38b_l3.png "Rendered by QuickLaTeX.com")
simplyfing we get
![\[{{x}^{2}}~+\text{ }{{y}^{2}}~-\text{ }27x\text{ }-\text{ }3y\text{ }+\text{ }142\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-371adbdcf678d7195b9a62949ea991aa_l3.png "Rendered by QuickLaTeX.com")
∴The equation of the circle is