2.
\((I)\)已知曲线\(C\):\(\dfrac{{x}^{2}}{4}+ \dfrac{{y}^{2}}{9}=1 \),直线\(l\):\(\begin{cases}x=2+t\;\;① \\ y=2-2t\;\;②\end{cases} \)\((t\)为参数\()\)
\((1)\)写出曲线\(C\)的参数方程,直线\(l\)的普通方程;
\((2)\)过曲线\(C\)上任意一点\(P\)作与\(l\)夹角为\(30^{\circ}\)的直线,交\(l\)于点\(A\),求\(\left| PA \right|\)的最大值与最小值.
\((II)\)若\(a > 0,b > 0,\)且\(\dfrac{1}{a}+\dfrac{1}{b}=\sqrt{ab}\)
\((1)\)求\({{a}^{3}}+{{b}^{3}}\)的最小值;
\((2)\)是否存在\(a,b\),使得\(2a+3b=6\)?并说明理由.