Let the equation of the required circle be (x – h)2 + (y – k)2 = r2.
Since the radius of the circle is 5 and its centre lies on the x-axis, k = 0 and r = 5.
Now, the equation of the circle becomes (x – h)2 + y2 = 25.
It is given that the circle passes through point (2, 3).
When h = –2, the equation of the circle becomes
(x + 2)2 + y2 = 25
x2 + 4x + 4 + y2 = 25 x2 + y2 + 4x – 21 = 0
When h = 6, the equation of the circle becomes
(x – 6)2 + y2 = 25
x2 – 12x +36 + y2 = 25
x2 + y2 – 12x + 11 = 0
