Since the circle is touching the X-axis, the radius of the circle is the Y co-ordinate of the centre.
∴ r = 3
The equation of a circle with centre at (h, k) and radius r is given by
(x – h)2 + (y – k)2 = r2
Here, h = -2, k = 3
The required equation of the circle is
⇒ (x + 2)2 + (y – 3)2 = 32
⇒ x2 + 4x + 4 + y2 – 6y + 9 = 9
⇒ x2 + y2 + 4x – 6y + 4 = 0
