The lines $4 x-3 y+2=0$ intersects the circle $x^2+y^2-2 x+6 y+c=0$ at two points $A, B$ and $A B=8$. If $(1, k)$ is a point on the given circle and $k>0$, then $k=$

If $2 x-3 y+5=0$ and $4 x-5 y+7=0$ are the equations of the normals drawn to a circle and $(2,5)$ is a point on the given circle, then the radius of the circle is

If $(\alpha, \beta)$ is the centre of the circle which passes through the point $(1,-1)$ and cuts the circles

$$ x^2+y^2+2 x-3 y-5=0, x^2+y^2-3 x+2 y+1=0 $$

orthogonally, then $\alpha-5 \beta=$

The centre of the circle touching the circles $x^2+y^2-4 x-6 y-12=0$

$x^2+y^2+6 x+18 y+26=0$ at their point of contact and passing through the point $(1,-1)$ is