Answer:

The general equation of a circle: (x – h)² + (y – k)² = r² …(i)

(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)

Putting (8, 1)

7h + k – 32 = 0..(iv)

Solving (iii)&(iv)

h = 5 and k = – 3

Centre = (5, – 3)

Radius = 25

(9, – 6) lies on the circle, (9 – 5)² + ( – 6 + 3)² = 5²

Hence, proved.