Question

Consider the region R = {(x,y)∈ R×R : x ≥ 0 and y2 ≤ 4 – x. Let F be the family of all circles that are contained in R and have centres on the x-axis. Let C be the circle that has the largest radius among the circles in F. Let (α, β) be a point where circle C meets the curve y2 = 4 – x.