The circle passing through point of intersection of the circle $S = 0$ and the line $P = 0$ is

If the two circles, $x^2 + y^2 + 2 g_1x + 2 f_1y = 0\, \& \,x^2 + y^2 + 2 g_2x + 2 f_2y = 0$ touch each then:

If the circles ${x^2} + {y^2} = 4,{x^2} + {y^2} – 10x + \lambda = 0$ touch externally, then $\lambda $ is equal to 

The two circles ${x^2} + {y^2} – 2x + 22y + 5 = 0$ and ${x^2} + {y^2} + 14x + 6y + k = 0$ intersect orthogonally provided $k$ is equal to

The centre of the smallest circle touching the circles $x^2 + y^2- 2y – 3 = 0$ and $x^2+ y^2 – 8x – 18y + 93 = 0$ is :