MathematicsHard127×since 2002Q3086Let A be the point (1,2)(1,2)(1,2) and B be any point on the curve x2+y2=16x^{2}+y^{2}=16x2+y2=16. If the centre of the locus of the point P, which divides the line segment AB\mathrm{AB}AB in the ratio 3:23: 23:2 is the point C(α,β)(\alpha, \beta)(α,β), then the length of the line segment AC\mathrm{AC}AC is :A355\frac{3 \sqrt{5}}{5}535B655\frac{6 \sqrt{5}}{5}565C255\frac{2 \sqrt{5}}{5}525D455\frac{4 \sqrt{5}}{5}545Check answerSkip