The general equation of a circle:
(x - h)2 + (y - k)2 = r2 …(i), where (h, k) is the centre and r is the radius.
Putting (1, 0) in (i)
(1 - h)2 + (0 - k)2 = r2
⇒h2 + k2 + 1 - 2h = r2 ..(ii)
Putting (2, - 7) in (i)
(2 - h)2 + ( - 7 - k)2 = r2
⇒h2 + k2 + 53 - 4h + 14k = r2
⇒ (h2 + k2 + 1 - 2h) + 52 - 2h + 14k = r2
h - 7k - 26 = 0..(iii) [from (ii)]
Similarly putting (8, 1)
7h + k - 32 = 0..(iv)
Solving (iii)&(iv)
h = 5 and k = - 3
centre(5, - 3)
Radius = 25
To check if (9, - 6) lies on the circle, (9 - 5)2 + ( - 6 + 3)2 = 52
Hence, proved.