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#349c154f-0c1a-4361-ab6e-d7bb70596091中等解答题椭圆标准方程与性质直线与圆+圆锥曲线

28.已知椭圆C:x2a2+y2b2=1(a>b>0)C:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)的离心率为33\frac{\sqrt{3}}{3},且过点(3,2)(\sqrt{3},\sqrt{2})
(1)求椭圆CC的方程;
(2)若椭圆CC的上顶点为PP,过PP的两条直线l1l_{1}l2l_{2}分别与CC交于异于点PPAABB两点,若直线l1l_{1}l2l_{2}的斜率之和为1-1,试判断直线ABAB是否过定点?若是,求出该定点;若不是,请说明理由.