Family of Circles - Practice Questions & MCQ

If the minimum radius of the circle which contains the three circles

Then the value of  must be

A square is inscribed in the circle . One side of the square is parallel to , then one vertex of the square is 

What is the equation of the circle that passes through the points 

Let the ellipse $E : \begin{aligned} & x^2+9y^2=9 \\ \end{aligned}$  intersect the positive x-and $y-axis$ at the points $A$ and $B$ respectively. Let the
major axis of $E$ be a diameter of the circle $C$. Let the line passing through $A$ and $B$ meet the circle $C$ at the
point $P$. If the area of the triangle with vertices $A, P$ and the origin $O$ is $\begin{aligned} & \frac{m}{n} \end{aligned}$ where $m$ and $n$ are coprime, then $m – n$ is equal to :

Equation of the circle touching the circle at the point and passing through the point is
 

 The equation of the circle having its centre on the line and passing through the point of intersection of the circle and is

If the distances from the origin to the centres of three circles are in G.P. then the lengths of the tangents drawn to them from any point on the circle are in

Tangents are drawn from any point on the circle to the circle . If the chord of contact touches the circle , then

The equation of the circle through the points of intersection of and touching the line is:

The equations of the three circles are:  and

. Find the coordinates of the point from which the length of tangents drawn to each of the three circles is equal.