# Tangential Curve

Calculus Level 5

Let $$t \in [0, 1]$$ be a parameter. Let $$\ell_t$$ be the line passing through the points $$(t,0)$$ and $$(0,1-t)$$.

For each value of $$a$$ we can define the point $$P_t$$ where $$\ell_t$$ intersects the neighboring lines $$\ell_{t+dt}$$.

The collection of points $$P_t$$ traces out a curve, as suggested in the drawing above. This curve satisfies the equation $$x^n + y^n = 1$$. Determine the value of $$n$$.

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