The radical axis of two circles and the line joining their centres are:

If the circles $x^2 + y^2 - 9 = 0$ and $x^2 + y^2 + 2ax + 2y + 1 = 0$ touch each other,then $a =$

The line $y=mx+c$ intersects the circle $x^2+y^2=r^2$ at two distinct points if:

For the circle $x^2 + y^2 - 2x + 4y - 4 = 0$,what is the line $2x - y - 1 = 0$?

The line $y = mx + c$ intersects the circle $x^2 + y^2 = r^2$ at two real distinct points,if

Suppose we have two circles of radius $2$ each in the plane such that the distance between their centers is $2 \sqrt{3}$. The area of the region common to both circles lies between