(本小題滿分13分)
已知
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是橢圓C的兩個焦點,
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、

為過
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的直線與橢圓的交點,且
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的周長為

.
(Ⅰ)求橢圓C的方程;
(Ⅱ)判斷
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是否為定值,若是求出這個值,若不是說明理由.
(Ⅰ)
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(Ⅱ)
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(Ⅰ)由橢圓定義可知,
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,

………2分
所以
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所以橢圓方程為
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…………………5分
(Ⅱ)設
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(1) 當直線斜率不存在時,有
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,
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,
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
………6分
(2) 當直線斜率存在時,設直線方程為
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代入橢圓方程,并整理得:
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…………7分
所以
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(或求出
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的值)
所以



………12分
所以
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………13分
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(本小題滿分12分)已知橢圓C:
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過點
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,且長軸長等于4.
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(Ⅱ)

是橢圓C的兩個焦點,⊙
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A、
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
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
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
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
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
直角三角形

的直角頂點

為動點,
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,
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為兩個定點,作
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于
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,動點
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滿足
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,當點
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運動時,設點

的軌跡為曲線

,曲線
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與
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.
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
的方程;
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m
的直線

,與曲線
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交于
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,
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兩點,且
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
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
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
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
.
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
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已知

是橢圓的兩個焦點,過

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
交橢圓于

,若

的周長為

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