MathematicsMedium175×since 2002Q2785Let S be the set of all the natural numbers, for which the line xa+yb=2{x \over a} + {y \over b} = 2ax+by=2 is a tangent to the curve (xa)n+(yb)n=2{\left( {{x \over a}} \right)^n} + {\left( {{y \over b}} \right)^n} = 2(ax)n+(by)n=2 at the point (a, b), ab ≠\ne= 0. Then :AS = ϕ\phiϕBn(S) = 1CS = {2k : k ∈\in∈ N}DS = NCheck answerSkip