Mathematics - Parabola Question with Solution | TestHub

Consider the region $R=\{(x,y)\in \mathbb{R}\times \mathbb{R}:x\ge 0$ 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 $y^2=4-x$.
The radius of the circles$C$is____.