2.
在平面直角坐标系\(xOy\)中,圆\(C_{1}\)的参数方程为\( \begin{cases} \overset{x=-1+a\cos \theta }{y=-1+a\sin \theta }\end{cases}(θ\)为参数,\(a\)是大于\(0\)的常数\().\)以坐标原点为极点,\(x\)轴正半轴为极轴建立极坐标系,圆\(C_{2}\)的极坐标方程为\(ρ=2 \sqrt {2}\cos (θ- \dfrac {π}{4})\).
\((1)\)求圆\(C_{1}\)的极坐标方程和圆\(C_{2}\)的直角坐标方程;
\((2)\)分别记直线\(l\):\(θ= \dfrac {π}{12}\),\(ρ∈R\)与圆\(C_{1}\)、圆\(C_{2}\)的异于原点的焦点为\(A\),\(B\),若圆\(C_{1}\)与圆\(C_{2}\)外切,试求实数\(a\)的值及线段\(AB\)的长.