Find the lengths of the intercepts made on the co-ordinate axes, by the circle $x^2 + y^2 – 5x + 13y – 14 = 0$

Show that the circles touch each other externally. Find their point of contact and the equation of their common tangent

$x^2+y^2–4x–10y+19=0$ and $x^2+y^2+2x+8y–23=0$

Show that the circles touch each other internally. Find their point of contact and the equation of their common tangent 

$x^2+y^2-4x-4y-28=0,x^2+y^2-4x-12=0$

Show that the circles touch each other internally. Find their point of contact and the equation of their common tangent

$x^2+y^2+4x-12y+4=0,x^2+y^2-2x-4y+4=0$.