9.
\((1)\)若数列\(\left\{ {{a}_{n}} \right\}\)的前\(n\)项和\({{S}_{n}}={{n}^{2}}+n+1\),则\({{a}_{n}}=\) ________________.
\((2)\)若椭圆\( \dfrac{x^{2}}{4}+ \dfrac{y^{2}}{k}=1\)的离心率\(e\)\(= \dfrac{2}{3}\),则实数\(k\)的取值是______________________.
\((3)\)某观测站在城\(A\)南偏西\(20^{\circ}\)方向的\(C\)处,由城\(A\)出发的一条公路,走向是南偏东\(40^{\circ}\),在\(C\)处测得公路距\(C\)处\(31\)千米的\(B\)处有一人正沿公路向城\(A\)走去,走了\(20\)千米后到达\(D\)处,此时\(C\)、\(D\)间的距离为\(21\)千米,问这人还要走千米可到达城\(A .\)
\((4)\)过点\(P(2,4)\)作两条互相垂直的直线分别交\(x\)轴、\(y\)轴于点\(A\)、\(B\),则线段\(AB\)的中点\(M\)的轨迹方程为____________________.