x² + y² + 2gx + 2fy + c = 0 is required circle

⇒   2g₁g₂ + 2f₁f₂ = c₁ + c₂

       0 + 0 = c + (–1)       ⇒      c = 1          .....(1)

and       x² + y² – 2x – 15 = 0

             2 (–1) g + 0 = 1 + (–15)

            – 2g = – 14

            g = 7                                             .....(2)

 $\therefore$        x² + y² + 14x + 2fy + 1 = 0 satisfies (0, 1)

              0 + 1 + 0 + 2f + 1 = 0       ⇒      f = – 1

 $\therefore$         Circle is  x² + y² + 14x – 2y + 1 = 0

 $\therefore$       Centre: (–7, 1)

 $\mathrm{r}=\sqrt{49+1-1}=7$

 $\therefore$        option (B), (C)