Let r be the radius of the largest circle passing through the focus (1,0) of y2=4x
Clearly, centre of the circle will be on X -axis and its coordinates are (1+r,0). The equation of the circle, is (x−1−r)2+y2=r2. It touches y2=4x. Therefore, the equation (x−r−1)2+4x=r2 must have equal roots ∴4(1−r)2−4(2r+1)=0 ⇒r=4 Hence, option (b) is correct.