已知橢圓
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的離心率
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,過點
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和
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的直線與原點的距離為

.
(1)求橢圓的方程.
(2)已知定點
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,若直線
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與橢圓交于
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兩點,試判斷:是否存在
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的值,使以
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為直徑的圓過點
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?若存在,求出這個值;若不存在,說明理由.
(1)
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,即
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.
過點
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的直線為
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,
把
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代入,即
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,
又由已知,得
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,解得
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.

所求方程為
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.
(2)設(shè)
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解
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消去

,得

.
必須

且

,
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或

①
要存在

的值使以

為直徑的圓過點
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,即要使
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,即要使

滿足①且使
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,
即使

②

,
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②式即

③

代入③得

.
又

滿足①,

存在

的值使以

為直徑的圓過

點,這個

的值是

.
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
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
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
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
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
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
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
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
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
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
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
:

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
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
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如圖,已知拋物線的方程為

,

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
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
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
所成的比為

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
所成的比為

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
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