\((1)\)等差数列\(\{a_{n}\}\),\(\{b_{n}\}\)的前\(n\)项和分别为\(S_{n}\)、\(T_{n}\),若\(\dfrac{{{S}_{n}}}{{{T}_{n}}}=\dfrac{2n}{n+1}\),则\(\dfrac{{{a}_{7}}}{{{b}_{5}}}=\)_____.
\((2)\)过点\((2,1)\)且在\(x\)轴上截距是在\(y\)轴上截距的两倍的直线的方程为______.
\((3)\)若圆\({{x}^{2}}+{{y}^{2}}={{r}^{2}}(r > 0)\)上仅有\(3\)个点到直线\(x-y-2=0\)的距离为\(1\),则实数\(r=\)_______.
\((4)\)已知\(\overrightarrow{OP} \),\(\overrightarrow{OQ} \)是非零不共线的向量,设\(\overrightarrow{OM}= \dfrac{1}{m+1} \overrightarrow{OP}+ \dfrac{m}{m+1} \overrightarrow{OQ} \),定义点集\(A=\left\{ \left.F \right| \dfrac{ \overrightarrow{FP}· \overrightarrow{FM}}{\left| \overrightarrow{FP}\right|}= \dfrac{ \overrightarrow{FQ}· \overrightarrow{FM}}{\left| \overrightarrow{FQ}\right|}\right\} \),当\({{F}_{1}}\),\({{F}_{2}}\in A\)时,若对于任意的\(m\geqslant 3\),不等式\(\left| \overrightarrow{{F}_{1}{F}_{2}}\right|\leqslant k\left| \overrightarrow{PQ}\right| \)恒成立,则实数\(k\)的最小值为__________.