Consider the region $$R = \left\{(𝑥, 𝑦) \epsilon R \times R ∶ x \geq 0  and  y^{2} \leq 4 − x \right\}$$. Let 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 F. Let ($$\alpha, \beta$$) be a point where the circle C meets the curve $$y^{2} = 4 − x$$.