Problem

Circles $C_1$ and $C_2$ have equations

$$x^2+y^2+6x-10y+18=0$$

and

$$(x-9)^2+(y+4)^2-64=0$$

respectively.

(a) Find the distance between the centres of the circles.

$P$ and $Q$ are points on $C_1$ and $C_2$ respectively. The distance between $P$ and $Q$ is denoted by $d$.

(b) Find the greatest and least possible values of $d$.