\((1)\)抛物线\(y=4{{x}^{2}}\)的准线方程为___________.
\((2)\)若“任意\(x∈R \),\({{x}^{2}}-2x-m > 0\)”是真命题,则实数\(m\)的取值范围是__________.
\((3)\)过抛物线\({{y}^{2}}=2px\left( p > 0 \right)\)的焦点\(F\)作倾斜角为\(45^{\circ}\)的直线交抛物线于\(A\)、\(B\)两点,若线段\(AB\)的长为\(8\),则\(p =\)___________.
\((4)\)已知圆\({{x}^{2}}+{{y}^{2}}-4x-9=0\)与\(y\)轴的两个交点\(A\),\(B\)都在某双曲线上,且\(A\),\(B\)两点恰好将此双曲线的焦距三等分,则此双曲线的标准方程为 .
\((5)\)如图,在空间四边形\(ABCD\)中,\(AC\)和\(BD\)为对角线,\(G\)为\(\triangle \)\(ABC\)的重心,\(E\)是\(BD\)上一点,\(BE=3ED \),以\(\{ \overset{⇀}{AB}, \overset{⇀}{AC}, \overset{⇀}{AD} \}\)为基底,则\(=\)__________.