HMMT 1998 K10

Calculus
Answer

Let $S$ be the locus of all points $(x, y)$ in the first quadrant such that $\frac{x}{t}+\frac{y}{1-t}=1$ for some $t$ with $0<t<1$ . Find the area of $S$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{1}{6}

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