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Determine the centre and radius of a circle

EXAMPLE 2 :

Given equation x  y  6x  4y  
2
2
9 0

Solution :

We can change the given equation into the standard form of

the circle by completing the square on x and y as follow

x  y  6x  4y      3  9  y  2  4  9
2
2
9 0
2
2

 
x

 x  6x  y  4y   9 (  ) 3  y  2   9  9  4
 
2
2
2
 
2
x
   6   2   6  2   4   2  4  2 2 2
 
 
          y          9  x  3  y  2   2 2
x


  2    2    2    2 