Properties of radical axis

Q.

The centre of circle passing through (0, 0) and (1, 0) and touching the circle $x^2+y^2=9$ is
(2002)

1. $\left(\begin{array}{c}\frac{1}{2},\frac{1}{2}\end{array}\right)$

2. $\left(\begin{array}{c}\frac{3}{1},\frac{1}{2}\end{array}\right)$

3. $\left(\begin{array}{c}\frac{1}{2},\sqrt{2}\end{array}\right)$

4. $\left(\begin{array}{c}\frac{1}{2},\frac{3}{2}\end{array}\right)$

Q.

If (h, k) is a point from which the tangents to the three circles $x^2+y^2-4x+7=0$, $2x^2+2y^2-3x+5y+9=0$ and $x^2+y^2+y=0$ are equal in length. Find the value of h + k ___ .

Q.

Which of the following statements is/are correct?

1. The radical axis of two circles is the locus of points whose power with respect to the two circles is equal.

2. The common point of intersection of the radical axes of three circles taken two at a time called the radical center of three circles.

1. None of these

2. Only 1

3. Only 2

4. Both 1 and 2