Find the equation to the circle which passes through the points `(1,2)(2,2)` and whose radius is `1.` Show that there are two such circles.

Explanation

Let the centre be (h,k)

`(x−h)^2+(y−k)^2=1`

or `(1−h)^2+(1−k)^2=1`

`=(2−h)^2+(2−k)^2=1, `

subtracting we get

`h+3=3∴k=3−h`

`(1−h)^2+(1−3+h)^2=1`

or` (1−h)^2+(h−2)^2=1`

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