# Tangential Network 1

Calculus Level 5

Let $$n$$ be a real number; define the curve $$C_n$$ by the equation

$x^n + y^n = 1.\ \ \ \ x, y \geq 0$

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

There exists one curve $$C_n$$ for which the value of $$\xi + \eta$$ is the same for all these tangent lines. How much is $$n$$?

×