Let the equation of the circle be
(x – h)2 + (y – k)2 = r2
center lies on x axis so let the center be (h, 0),
then (x – h)2 + y2 = 25
Since circle pass through (2, 3) we have;
(2 – h)2 + 32 = 25
⇒ (2 – h)2 = 16 ⇒ 2 – h = ±4
⇒ h = 6, -2
When h = 6 ; equation of circle is
(x – 6)2 + (y – 0)2 = 25
⇒ x2 + 36 – 12x + y2 = 25
⇒ x2 + y2 – 12x + 11 = 0
When h = -2; equation of circle is
(x + 2)2 + (y – 0)2 = 25
⇒ x2 + 4 + 4x + y2 = 25
⇒ x2 + y2 + 4x – 21 = 0
