$(1).\,\,\,$ $(x-a)^2+(y-b)^2$ $\,=\,$ $r^2$

$(2).\,\,\,$ $(x-h)^2+(y-k)^2$ $\,=\,$ $r^2$

$(3).\,\,\,$ $x^2+y^2$ $\,=\,$ $r^2$

The equation of a circle when the circle touches the $x$ axis.

$(x-a)^2+(x-b)^2 \,=\, b^2$

$(x-h)^2+(x-k)^2 \,=\, k^2$

The equation of a circle when the circle touches the $y$ axis.

$(x-a)^2+(x-b)^2 \,=\, a^2$

$(x-h)^2+(x-k)^2 \,=\, h^2$

$(1).\,\,$ $(x-a)^2+(y-a)^2$ $\,=\,$ $a^2$

$(2).\,\,$ $(x-b)^2+(y-b)^2$ $\,=\,$ $b^2$

$(3).\,\,$ $(x-r)^2+(y-r)^2$ $\,=\,$ $r^2$

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