Radius of the largest circle which passes through the focus of the parabola y 2 = 4 x and contained in it, is

Step-by-step solution

Let r be the radius of the largest circle passing through the focus 1 , 0 of y 2 = 4 x 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 + y 2 = r 2 . It touches y 2 = 4 x . Therefore, the equation x - r - 1 2 + 4 x = r 2 must have equal roots. ∴   4 1 - r 2 - 4 2 r + 1 = 0 ⇒ r = 4 Hence, option (b) is correct.