let radius of circle be r, its center lies on y-axis as y-axis bisects the 2 rays of y = |x|

Now vc 4 – ⇒

Note : The correct solution should be

due to symmetry center of the circle must be on y-axis

let center be (0, k)

Length of perpendicular from (0, k) to y = x,

(0, k) ls y = x

i.e. r =

∴ Equation of circle x 2 + (y – k) 2 =

solving circle and parabola 4 – y + y 2 – 2ky + = 0

y 2 – (2k + 1) y + = 0

Because circle touches the parabola D

D = 0

(2k + 1) 2 = 4

4k 2 + 4k + 1 = 2k 2 + 16

On solving we get k =

Therefore radius k = ≈ 1.3546

However among the given choices the following method will yield one of the choice.