MathDB

In the plane with orthogonal Cartesian coordinates

x

and

y

, prove that the line whose equation is

ux+vy = 1

will be tangent to the cirve

x^m+y^m=1

(where

m>1

) if and only if

u^n + v^n = 1

and

m^{-1} + n^{-1} = 1

Problem Statement