Question

If a circle with radius 2 units touches the x-axis at (1, 0) then its center may be:

Answer 1

If x² + y² + 2gx + 2fy + c = 0 touches x−axis

 then r = |f| where r is radius of cirlce and (−g, −f) is centre of circle

Given that r = 2

⇒ ∣f∣ = 2

⇒ f = ±2

Cirlce touches x-axis at (1,0),

Hence centre of cirlce may be (1, 5) or (1, −2).