Find the equation of the circle which touches the coordinate axes and whose centre lies on the line `x-2y=3.`

Explanation

If the circle lies in the third quadrant, then its centre will be `(-a,-a)`.

The centre lies on `x-2 y=3`.

`therefore-a+2 a=3 Rightarrow a=3`

`therefore` Required equation of the circle `=(x+3)^{2}+(y+3)^{2}=9`

`=x^{2}+y^{2}+6 x+6 y+9=0`

If the circle lies in the fourth quadrant, then its centre will be `(a,-a)`,

`therefore a+2 a=3 Rightarrow a=1`

`therefore` Required equation of the circle `=`

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