已知\(A\left(-1,2\right) \)为曲线\(C:y=2{x}^{2} \)上的点,直线\({l}_{1} \)过点\(A\),且与曲线\(C\)相切,直线\({l}_{2}:x=a\left(a > -1\right) \)交曲线\(C\)于\(B\),交直线\({l}_{1} \)于点\(D\).
\((1)\)求直线\({l}_{1} \)的方程;
\((2)\)设\(∆BAD \)的面积为\({S}_{1} \),求\({S}_{1} \)的值;
\((3)\)设由曲线
,直线\({l}_{1} \),\({l}_{2} \)所围成的图形的面积为\({S}_{2} \),求证\({S}_{1}:{S}_{2} \)的值为与\(a\)无关的常数.