Radius of circle touching $y-$axis at point $P(0,2)$ and circle $x^2 + y^2 = 16$ internally-

Let a circle $C_1 \equiv  x^2 + y^2 - 4x + 6y + 1 = 0$ and circle $C_2$ is such that it's centre is image of centre of $C_1$ about $x-$axis and radius of $C_2$ is equal to radius of $C_1$, then area of $C_1$ which is not common with $C_2$ is -

Let the latus ractum of the parabola $y ^{2}=4 x$ be the common chord to the circles $C _{1}$ and $C _{2}$ each of them having radius $2 \sqrt{5}$. Then, the distance between the centres of the circles $C _{1}$ and $C _{2}$ is

If one of the diameters of the circle $x^{2}+y^{2}-2 \sqrt{2} x$ $-6 \sqrt{2} y+14=0$ is a chord of the circle $(x-2 \sqrt{2})^{2}$ $+(y-2 \sqrt{2})^{2}=r^{2}$, then the value of $r^{2}$ is equal to

The circles ${x^2} + {y^2} = 9$ and ${x^2} + {y^2} - 12y + 27 = 0$ touch each other. The equation of their common tangent is 

If the circles of same radius a and centers at $(2, 3)$ and $(5, 6)$ cut orthogonally, then $a =$