A circle is given by x2 (y – 1)2= 1, another circle C touches it externally and also the x-axis,then the locus of its centre is?

• A. {(x, y) : x2 = 4y} ∪ {(x, y) : y ≤ 0}
• B. {(x, y) : x2 + (y – 1)2 = 4} ∪ {x, y) : y ≤ 0}
• C. {(x, y) : x2 = y} ∪ {(0, y) : y ≤ 0}
• D. {(x, y) : x2 = 4y} ∪ {(0, y) : y ≤ 0}