If the circle cuts each of the circles

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

If the circle

x^2 + y^2 + 2gx + 2fy + c = 0

cuts each of the circles

x^2 + y^2 - 4 = 0

x^2 + y^2 - 6x - 8y + 10 = 0

and

x^2 + y^2 + 2x - 4y - 2 = 0

at the extremities of a diameter, then (1)

c = -4

(2)

g + f = c - 1

(3)

g^2 + f^2 - c = 17

(4)

gf = 6