过直线\(x+y+2=0\)上一点\(P\)，作圆\((x-3) ^{2} +(y+1) ^{2} =16\)的两条切线，切点分别为\(A(x _{1} , y _{1} )\)，\(B(x _{2} , y _{2} )\)，若\(y _{2} ^{2} -y _{1} ^{2} =(x _{1} -x _{2} )(x _{1} +x _{2} -2)\)，则\(|PA|= (\:\:\:\:)\)
A. \(8\)
B. \(4 \sqrt {5}\) C. \(4 \sqrt {13}\) D. \(10\)
