Find the equation of the circle which touches x-axis and whose centre is (1, 2).

Given that, circle with centre (1,2) touches x-axis.

Radius of the circle is, r = 2

So, the equation of the required circle is:

(x – l)² + (y – 2)² = 2²

=>x² -2x + 1 + y² -4y + 4 = 4

=> x² + y² – 2x-4y + 1 = 0

Since the circle has a centre (1, 2) and also touches x-axis.

Radius of the circle is, r = 2

The equation of a circle having centre (h, k), having radius as r units, is

(x – h)² + (y – k)² = r²

So, the equation of the required circle is:

(x – 1)² + (y – 2)² = 2²

⇒x² – 2x + 1 + y² – 4y + 4 = 4

⇒ x² + y² – 2x – 4y + 1 = 0

The equation of the circle is x² + y² – 2x – 4y + 1 = 0.