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Show that |(z-2)/(z-3)|=2 represents a c...

Show that `|(z-2)/(z-3)|=2` represents a circle. Find its centre and radius.

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The correct Answer is:
Centre `-=(10//3,0); "Radius" = 2//3`
`|(z-2)/(z-3)| =2`
`rArr |z-2|^(2) = 4|z-3|^(2)`
`rArr |x-2+iy|^(2) = 4|x-3+iy|^(2)`
`rArr(x-2)^(2) + y^(2) = 4[(x-3)^(2) +y^(2)]`
`rArr 3x^(2) + 3y^(2) -(20)/(3)x + (32)/(3) =0`
`rArr x^(2) + y^(2) -(20)/(3)x + (32)/(3) = 0`
`rArr (x-(10)/(3))^(2) + y^(2) = (4)/(9)`
Thus,distance of (x,y) from the point (10/3,0) is 2/3.
So,centre of the circle is (10/3,0) and rasius is 2/3.
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