Tangential Network 1

Calculus Level 5

Let nn be a real number; define the curve CnC_n by the equation

xn+yn=1.    x,y0x^n + y^n = 1.\ \ \ \ x, y \geq 0

For every point x,yx, y on CnC_n there is a tangent line. This tangent line intersects the coordinate axes in points (ξ,0)(\xi,0) and (0,η)(0,\eta), respectively.

There exists one curve CnC_n for which the value of ξ+η\xi + \eta is the same for all these tangent lines. How much is nn?


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