题目内容
设P是椭圆
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【答案】分析:先根据椭圆方程设出P的参数坐标,求得A,F的坐标,进而分别表示出
,
,
代入
化简整理求得其最小值.
解答:解:P的参数坐标为(5cosθ,4sinθ);
坐标A(-5,0);F(3,0);
则
=(-5-5cosθ,0-4sinθ);
=(3-5cosθ,0-4sinθ);
则
=(-5-5cosθ)•(3-5cosθ)+16sin2θ+
(-5-5cosθ,-4sinθ)•(8,0)
=(-5-5cosθ)(3-5cosθ)+16sin2θ+2(-5-5cosθ)
=9cos2θ-9≥-9.
故答案为:-9.
点评:本题主要考查了椭圆的应用,参数坐标的应用.考查了学生综合分析问题和解决问题的能力.
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解答:解:P的参数坐标为(5cosθ,4sinθ);
坐标A(-5,0);F(3,0);
则
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则

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=(-5-5cosθ)(3-5cosθ)+16sin2θ+2(-5-5cosθ)
=9cos2θ-9≥-9.
故答案为:-9.
点评:本题主要考查了椭圆的应用,参数坐标的应用.考查了学生综合分析问题和解决问题的能力.

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