Question:

The locus of the centres of the circles which touch the circle x² + y² = 1 externally, also touch the y-axis and lie in the first quadrant is:

y=√1+2x, x≥0

y=√1+4x, x≥0

x=√1+4y, y≥0

x=√1+2y, y≥0

The correct option is y=√1+2x, x≥0
√h²+k²=|h|+1 ⇒x²+y²=x²+1+2x ⇒y²=1+2x ⇒y=√1+2x; x≥0