Correct option (B)(D)
Explanation:
Let S = x2 + y2 + 2gx + 2fy + c = 0
∴ it cuts x2 + y2 = 4 orthogonally
⇒ c = 4
Moreover - 2g + 2f + 9 = 0
∴ (- g, - f) satisfy the given equation)
∴ S = x2 + y2 + 2gx + 2fy + 4 = 0
⇒ x2 + y2 + (2f + 9)x + 2fy + 4 = 0
⇒ (x2 + y2 + 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).