已知双曲线\(C: \dfrac{{{x}^{2}}}{{{a}^{2}}}-\dfrac{{{y}^{2}}}{{{b}^{2}}}=1\)，\(( a > 0 , b > 0 )\)的左\(､\)右焦点分别为\({{F}_{1}}\)，\({{F}_{2}}\)，\(O\)为坐标原点，\(P\)是双曲线在第一象限上的点，\(\overrightarrow{\left| P{{F}_{1}} \right|}=2\overrightarrow{\left| P{{F}_{2}} \right|}=2m\)，\(( m > 0 )\)，\(\overrightarrow{P{{F}_{1}}}\cdot \overrightarrow{P{{F}_{2}}}={{m}^{2}}\)，则双曲线\(C\)的渐近线方程为\((\:\:\:\:)\)
A. \(y=\pm \dfrac{1}{2}x\)
B. \(y=\pm \dfrac{\sqrt{2}}{2}x\) C. \(y=\pm x\) D. \(y=\pm \sqrt{2}x\)
