# Tangential Curve

**Calculus**Level 5

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 \(n\).