Condition on $k$ for $x^2+y^2-12x-6y-4=0$ and $x^2+y^2-4x-12y-k=0$ to have simultaneous solutions $(x,y)$ The two equations: $$x^2+y^2-12x-6y-4=0$$ and $$x^2+y^2-4x-12y-k=0$$ 
have simultaneous real solutions $(x,y) \iff a \le k\le b$.
 Then, what is the value of $a+b$? 

let x^2+y^2-12x-6y-4=0 is A 
and let x^2+y^2-4x-12y-k=0 is B
considering A-B equals -8x+6y+k-4
and “A and B is equivalent to A and A-B” 
so we just consider k’s condition that A and A-B have simultaneous real solutions .
Ais a circle that center is (6,3) and radius is 7 
so A and A-B have simultaneous real solutions is circle A and line A-B have common point.
consider “the length between circle center and line A-B”
and the circle radius ,we can get the condition of k so get a+b.
