Question

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

Answer 1

Since the circle whose centre is (1, 2) touch x-axis

So, the equation of the circle is (x – h)² + (y – k)² = r²

⇒ (x – 1)² + (y – 2)² = (2)²

⇒ x² – 2x + 1 + y² – 4y + 4 = 4

⇒ x² + y² – 2x – 4y + 1 = 0

Hence, the required equation is x² + y² – 2x – 4y + 1 = 0.