JEE Advanced 2021 · Paper 2, Mathematics question 8

Question Stem for Question Nos. 7 and 8

Consider the region $R = \{(x, y) \in \mathbb R \times \mathbb R : x \ge 0 \text{ and } y^2 \le 4 - x\}$. Let $\mathcal F$ be the family of all circles that are contained in $R$ and have centers on the $x$-axis. Let $C$ be the circle that has largest radius among the circles in $\mathcal F$. Let $(\alpha, \beta)$ be a point where the circle $C$ meets the curve $y^2 = 4 - x$.