Let the locus of the centre (α, β), β > 0, of the circle which touches the circle x2 + (y – 1)2 = 1 externally and also touches the x - axis be L. Then the area bounded by L and the line y = 4 is :
1
\(\frac{32 \sqrt{2}}{3}\)
2
\(\frac{40 \sqrt{2}}{3}\)
3
\(\frac{64}{3}\)
4
\(\frac{32}{3}\)