A Constrained Distance Max

★ 7/10Extrema analytic geometry inequality Casework

Problem

Let $a$ be a positive constant, and consider the segment

ax + y = 2a + 3, \qquad x \geqslant 0,\ y \geqslant 0.

Let $S$ be the maximum value of $x^2 + y^2$ on this segment. If $S \in [49, 121]$ , find the range of possible values of $a$ .

Answer

Solution

Difficulty	7/10
Topics	Extrema, analytic geometry, inequality, Casework

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