**(B) radius of S is 7 **

**(C) center of S is (-7, 1) **

Given circles

x^{2} + y^{2} - 2x - 15 = 0

x^{2} + y^{2 }- 1 = 0

Radical axis x + 7 = 0 … (1)

Centre of circle lies on (1)

Let the centre be (-7, k)

Let equation be x^{2} + y^{2} + 14x - 2ky + c = 0

Orthogonallity gives

-14 = c -15 ⇒ c = 1 … (2)

(0, 1) → 1 - 2k + 1 = 0 ⇒ k = 1