Two particles move in the $xy$-plane. At time $t$, the position of particle $A$ is given by $x(t) = 5 t - 5$ and $y(t) = 4 t - k$, and the position of particle $B$ is given by $x(t) = 4 t$ and $y(t) = t^2 - 2t - 1$.

(a) If $k = 9$, do the particles ever collide?

(b) Find $k$ so that the two particles are certain to collide.
$k =$