If a circle passes through the point (0, 0) (a, 0), (0, b) then find the coordinates of its centre.
The equation of a circle having centre (h,k), having radius as "r" units, is
(x – h)2 + (y – k)2 = r2
Putting the values of given co-ordinates in the above expression,
(0,0)
(0 – h)2 + (0 – k)2 = r2
h2 + k2 = r2
(a,0)
(a – h)2 + (0 – k)2 = r2
a2 + h2 - 2ah + k2 = r2 ------ (1)
(0,b)
(0 – h)2 + (b – k)2 = r2
h2 + b2 + k2 - 2bk = r2 ------- (2)
On solving equations (1) & (2), respectively,
a (a – 2h) = 0
b (b – 2k) = 0
So,
a = 0 or 2h
b = 0 or 2k respectively.
Since the circle passes through the centre (0,0), so the co – ordinates are
a = 2h,
b = 2k,
Th co – ordinates of the centre are 
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