Word Count : 391

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To check whether the set \[ S = \{(x,y) : x^2 + y^2 \leq 1, \quad y^2 \geq x \} \] is convex, we need to verify whether for any two points \((x_1, y_1) \in S\) and \((x_2, y_2) \in S\), the entire line segment joining them is also contained in \( S \). ### Step 1: Understanding the Constraints - The first constraint, \( x^2 + y^2 \leq 1 \), represents a filled unit disk centered at ____ ______ _______ _______ ___ ______ ___ _____ ______ ________.
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