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. 

3. 

4. 36

Q.

The centre of the circle passing through the point (0, 1) and touching the curve $y=x^2$ at (2, 4) is

1. 

2. 

3. 

4. None of these

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. The equation of the circle passing through $(1,1)$ and the points of intersection of $x^2+y^2+13x-3y=0$ and $11x+\frac{1}{2}y+\frac{25}{2}=0$ is $S.$ Then point $(2,2)$ is

1. lying on the circle $S$
2. centre of circle $S$
3. lying inside the circle $S$
4. lying outside the circle $S$

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. $5$