Equation of Family of Circles Passing through Points of Intersection of Circle and a Line

Q.

Consider the family of circles $x^2+y^2-2x-2\lambda y-8=0$ passing through two fixed points A and B. Then the distance between the points A and B, is $\underset{–}{}$

1. 6

2. $\sqrt{6}$

3. $\sqrt{18}$

4. 36

Q. If a circle $C$ passing through the point $(4,0)$ touches the circle $x^2+y^2+4x-6y=12$ externally at the point $(1,-1)$ then the radius of $C$ is :

1. $\sqrt{57}$
2. $4$
3. $2\sqrt{5}$
4. $5$