The two circles $x^2 + y^2 - 4y = 0$ and $x^2 + y^2 - 8y = 0$:

$A$ line $y=mx+1$ intersects the circle $(x-3)^2+(y+2)^2=25$ at the points $P$ and $Q$. If the midpoint of the line segment $PQ$ has $x$-coordinate $-\frac{3}{5}$,then which one of the following options is correct?

Two circles $x^2 + y^2 = ax$ and $x^2 + y^2 = c^2$ touch each other if:

The power of a point $(2,0)$ with respect to a circle $S$ is $-4$ and the length of the tangent drawn from the point $(1,1)$ to $S$ is $2$. If the circle $S$ passes through the point $(-1,-1)$,then the radius of the circle $S$ is

The area of the circle centered at $(1, 2)$ and passing through $(4, 6)$ is

Area of the circle in which a chord of length $\sqrt{2}$ makes an angle $\frac{\pi}{2}$ at the centre is