Find the equation of the circle passing through `(1,0)a n d(0,1)` and having the smallest possible radius.

Explanation

Let the equation of circle is :
`x^2+y^2+2gx+2fy+c=0`

This passes through (1,0) and (0,1), therefore,

`1+2g+c=0` and

`1+2f+c=0`

`=>g=f` and `c=−2g−1`

Radius r of circle is given by :

`r^2=g^2+f^2−c`

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