# Multiple methods would work

Geometry Level 4

Through the point $$(\alpha,\beta)$$, where $$\alpha \beta > 0$$, the straight line $$\dfrac{x}{a} + \dfrac{y}{b} = 1$$ is drawn so as to form with the coordinate axes a triangle of area $$S$$. If $$a,b > 0$$ is the least value of $$S$$ is:

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