Circles a justification please...

Wen we r given to find the equation of a circle thru three given points, we go by the family approach..we tend to form the equation of the circle taking the first two points as the end point of the diameter nd den form a strait line eq..we then take the eq of the circle passing thru their intersection as - C[1] + K L[1]=0..put in the the third point nd get the reqd value...now my qs is how can we tek the first two points to be the end points of the diameter??

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