If the circles $x^2 + y^2 = 16$ and $x^2 + y^2 + 2ax + 4y + 4 = 0$ touch each other internally, then $a =$

If the lengths of the tangents drawn from a point $P$ to the circles $x^2+y^2-8x+40=0$,$5x^2+5y^2-25x+80=0$,and $x^2+y^2-8x+16y+160=0$ are equal,then the coordinates of point $P$ are:

If one of the diameters of the curve $x^{2}+y^{2}-4x-6y+9=0$ is a chord of a circle with centre $(1,1)$, the radius of this circle is

Where do the circles $x^2 + y^2 + 2x - 2y + 1 = 0$ and $x^2 + y^2 - 2x - 2y + 1 = 0$ touch each other?

Find the equation of a circle with radius $5$ units and touching the circle $x^2+y^2-2x-4y-20=0$ at the point $(5,5)$.

If the circle $S=0$ intersects the three circles $S_1 \equiv x^2+y^2+4x-7=0$,$S_2 \equiv x^2+y^2+y=0$ and $S_3 \equiv x^2+y^2+\frac{3}{2}x+\frac{5}{2}y-\frac{9}{2}=0$ orthogonally,then the radical axis of $S=0$ and $S_1=0$ is