**Correct option (B)(D)**

**Explanation:**

Let S = x^{2} + y^{2} + 2gx + 2fy + c = 0

∴ it cuts x^{2} + y^{2} = 4 orthogonally

⇒ c = 4

Moreover - 2g + 2f + 9 = 0

∴ (- g, - f) satisfy the given equation)

∴ S = x^{2} + y^{2} + 2gx + 2fy + 4 = 0

⇒ x^{2} + y^{2} + (2f + 9)x + 2fy + 4 = 0

⇒ (x^{2} + y^{2} + 9x + 4) + 2f (x + y) = 0

It is of the form S + λP = 0 and hence passes through the intersection of S = 0 and P = 0 which when solved give (-1/2, 1/2), (-4, 4).