The circle touches both the x and y axes in the first quadrant and the radius is a.
For a circle of radius a, the centre is (a, a).
The equation of a circle having centre (h, k), having radius as r units, is
![\[{{\left( x\text{ }-\text{ }h \right)}^{2}}~+\text{ }{{\left( y\text{ }-\text{ }k \right)}^{2}}~=\text{ }{{r}^{2}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8c4257135d60ab7249e3b68dac5b3fde_l3.png "Rendered by QuickLaTeX.com")
Hence, the equation of the circle is
![\[\begin{array}{*{35}{l}} {{\left( x\text{ }-\text{ }a \right)}^{2}}~+\text{ }{{\left( y\text{ }-\text{ }a \right)}^{2}}~=\text{ }{{a}^{2}} \\ {{x}^{2}}~\text{ }-2ax\text{ }+\text{ }{{a}^{2}}~+\text{ }{{y}^{2}}~\text{ }-2ay\text{ }+\text{ }{{a}^{2}}~-\text{ }{{a}^{2}}~=\text{ }0 \\ {{x}^{2}}~\text{ }-2ax\text{ }+\text{ }{{y}^{2}}~\text{ }-2ay\text{ }+\text{ }{{a}^{2}}~=\text{ }0 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-bfd2160ca28a3a43a6c213a0afe7fc04_l3.png "Rendered by QuickLaTeX.com")