Yes, there are many methods to find the equation; the easiest being the process of solving the eqn. of circle putting the three points. But what I didn't understand is the another method which my book describes as:

> 
> If three points be $A$ , $B$ , $C$ , then write $S$ = equation of circle on $AB$ as diameter.
>  $P$ = equation of line through $A$, $B$ .
> 
> 
> 

The required equation of the circle is $$ S + \lambda . P = 0$$ , where $\lambda$ is found by passing it through the point $C$ .

What did the book do here?? Why should the circle have $AB$ as diameter and how does the equation represent the circle passing through $A , B , C$ ? It chose a circle having $AB$ as diameter. But the circles passing through these three points can have any diameter. So, why $AB$? How can the equation be the equation of the required circles?