题型:解答题 题类:模拟题 难易度:难
在直角坐标系\(xOy\)中,以坐标原点\(O\)为极点,以\(x\)轴正半轴为极轴,建立极坐标系,直线\({{l}_{1}}\)的极坐标方程为\(\rho =\dfrac{-1}{{\sin }\theta +a{\cos }\theta }\),\({{l}_{2}}\)的极坐标方程为\(\rho =\dfrac{1}{{\cos }\theta -a{\sin }\theta }\).
\((1)\)求直线\({{l}_{1}}\)与\({{l}_{2}}\)的交点的轨迹\(C\)的方程;
\((2)\)若曲线\(C\)上存在\(4\)个点到直线\({{l}_{1}}\)的距离相等,求实数\(a\)的取值范围.