MathematicsHard94×since 2002Q2845Let the locus of the centre (α,β),β>0(\alpha, \beta), \beta>0(α,β),β>0, of the circle which touches the circle x2+(y−1)2=1x^{2}+(y-1)^{2}=1x2+(y−1)2=1 externally and also touches the xxx-axis be L\mathrm{L}L. Then the area bounded by L\mathrm{L}L and the line y=4y=4y=4 is:A3223\frac{32 \sqrt{2}}{3}3322B4023\frac{40 \sqrt{2}}{3}3402C643\frac{64}{3}364D323\frac{32}{3}332Check answerSkip