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The locus of the centres of the circles, which touch the circle, x 2 + y 2 = 1 externally, also touch the y-axis and lie in the first quadrant, is

1. x = y 2 1 + , y ≥ 0
2. y = x 2 1 + , x ≥ 0
3. y = x 4 1 + , x ≥ 0
4. x = y 4 1 + , y ≥ 0

Correct answer: y = x 2 1 + , x ≥ 0

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