Circle

Since C be the circle that has largest radius so, it touches the y-axis at (0,0) and centre at x-axis.
Let the equation of circle be x2+y2+λx=0
For point of intersection of circle\;parabola y2=4−x.
x2+4−x+λx=0
⇒x2+x(λ−1)+4=0‌‌... (i)
For tangency: ∆=0
⇒(λ−1)2−16=0
⇒λ=5 (rejected) or λ=−3
∴‌‌ Equation of circle :x2+y2−3x=0
Radius =‌

3

2

=1.5