find the center of the circle passing through points (1, 4) , (4, 1) and(-2, 1) is
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Let (a,b) be the centre
So (a-1)^2 + (b-4)^2 = (a+2)^2+(b-1)^2
-2a+1 + 16 -8b=4a+4 -2b+1
-6a= 6b -12
a=-b+2 Eq1
Now
(a-1)^2+b-4)^2 = (a-4)^2+(b-1)^2
-2a+1-8b+16 = -8a+16 -2b+1
6a=6b
a=b
So a=b=1
Hence Cetre is(1,1)
So (a-1)^2 + (b-4)^2 = (a+2)^2+(b-1)^2
-2a+1 + 16 -8b=4a+4 -2b+1
-6a= 6b -12
a=-b+2 Eq1
Now
(a-1)^2+b-4)^2 = (a-4)^2+(b-1)^2
-2a+1-8b+16 = -8a+16 -2b+1
6a=6b
a=b
So a=b=1
Hence Cetre is(1,1)
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