The sides of a squares are x = 6, x = 9, y = 3 and y = 6.
assuming A, B, C, D be the vertices of the square. we get, the coordinates as: A = (6, 3)
B = (9, 3)
C = (9, 6)
D = (6, 6)
the equation of the circle with diagonal AC is given by
![\[\begin{array}{*{35}{l}} (x\text{ }-\text{ }{{x}_{1}})\text{ }(x\text{ }-\text{ }{{x}_{2}})\text{ }+\text{ }(y\text{ }-\text{ }{{y}_{1}})\text{ }(y\text{ }-\text{ }{{y}_{2}})\text{ }=\text{ }0 \\ \left( x\text{ }-\text{ }6 \right)\text{ }\left( x\text{ }-\text{ }9 \right)\text{ }+\text{ }\left( 4\text{ }-\text{ }3 \right)\text{ }\left( 4\text{ }-\text{ }6 \right)\text{ }=\text{ }0 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8f20e8106ab0118f8951e9ecd3f542ec_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}} {{x}^{2}}~-\text{ }6x\text{ }-\text{ }9x\text{ }+\text{ }54\text{ }+\text{ }{{y}^{2}}~-\text{ }3y\text{ }-\text{ }6y\text{ }+\text{ }18\text{ }=\text{ }0 \\ {{x}^{2}}~+\text{ }{{y}^{2}}~-\text{ }15x\text{ }-\text{ }9y\text{ }+\text{ }72\text{ }=\text{ }0 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-64d5ccfeda306d89b5c79fc50b3b595c_l3.png "Rendered by QuickLaTeX.com")
We know that the equation of the circle with diagonal BD as diameter is given by
![\[\begin{array}{*{35}{l}} (x\text{ }-\text{ }{{x}_{1}})\text{ }(x\text{ }-\text{ }{{x}_{2}})\text{ }+\text{ }(y\text{ }-\text{ }{{y}_{1}})\text{ }(y\text{ }-\text{ }{{y}_{2}})\text{ }=\text{ }0 \\ \left( x\text{ }-\text{ }9 \right)\text{ }\left( x\text{ }-\text{ }6 \right)\text{ }+\text{ }\left( y\text{ }-\text{ }3 \right)\text{ }\left( y\text{ }-\text{ }6 \right)\text{ }=\text{ }0 \\ {{x}^{2}}~-\text{ }9x\text{ }-\text{ }6x\text{ }+\text{ }54\text{ }+\text{ }{{y}^{2}}~-\text{ }3y\text{ }-\text{ }6y\text{ }+\text{ }18\text{ }=\text{ }0 \\ {{x}^{2}}~+\text{ }{{y}^{2}}~-\text{ }15x\text{ }-\text{ }9y\text{ }+\text{ }72\text{ }=\text{ }0 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c5682a145807575952b37e323c1f30a0_l3.png "Rendered by QuickLaTeX.com")
∴The equation of the circle is x2 + y2 – 15x – 9y + 72 = 0