A triangle has vertices \(P_{}^{}=(-8,5)\), \(Q_{}^{}=(-15,-19)\), and \(R_{}^{}=(1,-7)\). The equation of the bisector of \(\angle P\) can be written in the form \(ax+2y+c=0_{}^{}\). Find \(a+c_{}^{}\).

(第八届AIME1990 第7题)