Find the equation of a circle which pass through the points O (0, 0), A (4, 0) and B (0, 3).

Let the equation of the circle be                        ...(i)
Since it passes through (0, 0)
∴                                         ...(ii)
Since it passes through (4, 0)
∴                       ...(iii)
But, from (ii),          
∴ From (iii), we have 
Since it passes through (0, 3)
∴      
∴ From (ii), we have
                          
or              
Hence, the equation of circle is: 
or  
or