在平面直角坐標(biāo)系
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中,橢圓

的中心為坐標(biāo)原點(diǎn),左焦點(diǎn)為
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,
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為橢圓

的上頂點(diǎn),且
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.
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(Ⅰ)求橢圓

的標(biāo)準(zhǔn)方程;
(Ⅱ)已知直線

:

與橢圓

交于
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,
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兩點(diǎn),直線
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:
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(
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)與橢圓
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交于
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,
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兩點(diǎn),且
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,如圖所示.
(�。┳C明:
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;
(ⅱ)求四邊形
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的面積
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的最大值.
(Ⅰ)解:設(shè)橢圓
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的標(biāo)準(zhǔn)方程為
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.
因?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823210917641543.png" style="vertical-align:middle;" />,
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,
所以
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.
所以
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. ………………………………………2分
所以 橢圓
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的標(biāo)準(zhǔn)方程為
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. ………………………………………3分
(Ⅱ)設(shè)
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,
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,
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,
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.
(�。┳C明:由
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消去
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得:
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.
則
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,

………………………………………5分
所以
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


.
同理

. ………………………………………7分
因?yàn)?

,
所以
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.
因?yàn)?

,
所以
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. ………………………………………9分
(ⅱ)解:由題意得四邊形

是平行四邊形,設(shè)兩平行線
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間的距離為

,則

.
因?yàn)?

,
所以
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. ………………………………………10分
所以
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
.
(或

)
所以 當(dāng)

時(shí), 四邊形

的面積

取得最大值為

.
………………………………………13分
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如圖,橢圓

的離心率為
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
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所圍成的矩形ABCD的面積為8.
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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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內(nèi)分成了
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
的直線

交橢圓于不同兩點(diǎn)

、
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,且

,當(dāng)

的面積最大時(shí),求直線

的方程.

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橢圓

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
( )
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若點(diǎn)F
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2為橢圓
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的焦點(diǎn),P為橢圓上的點(diǎn),當(dāng)
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的面積為1時(shí),
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的值是( )
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