BITSAT 2018 Slot 2 Solved Paper

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.