The number of common tangents of the circles given by $x^2 +y^2 - 8x - 2y + 1 = 0$ and $x^2 + y^2 + 6x + 8y = 0$ is

The value of k so that ${x^2} + {y^2} + kx + 4y + 2 = 0$ and $2({x^2} + {y^2}) - 4x - 3y + k = 0$ cut orthogonally is

If the circles $(x+1)^2+(y+2)^2=r^2$ and $x^2+y^2-4 x-4 y+4=0$ intersect at exactly two distinct points, then

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

If the circles ${x^2} + {y^2} - 2ax + c = 0$ and ${x^2} + {y^2} + 2by + 2\lambda = 0$ intersect orthogonally, then the value of $\lambda $ is

If the circle ${x^2} + {y^2} + 6x - 2y + k = 0$ bisects the circumference of the circle ${x^2} + {y^2} + 2x - 6y - 15 = 0,$ then $k =$