职教组卷基于海量职教高考试题库建立的在线组卷及学习系统
职教组卷
  • 题型:解答题 题类:月考试卷 难易度:中档

    已知\(F _{1}\),\(F _{2}\)分别为椭圆\(C\):\( \dfrac {x^{2}}{a^{2}} + \dfrac {y^{2}}{b^{2}} =1(a > b > 0)\)的左右焦点,点\(P ( \dfrac { \sqrt {6}}{2}, \dfrac {1}{2})\)在椭圆\(C\)上,且\(|PF _{l} |+|PF _{2} |=2 \sqrt {2}\).
    \((1)\)求椭圆\(C\)的方程;
    \((2)\)设\(A\)为椭圆\(C\)的左顶点,过点\(F _{2}\)的直线\(l\)椭圆\(C\)于\(M\),\(N\)两点,记直线\(AM\),\(AN\)的斜率分别为\(k _{1}\),\(k _{2}\),若\(k _{1} +k _{2} =3\),求直线\(l\)方程.
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