如右圖,設(shè)由拋物線
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與過它的焦點F的直線
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所圍成封閉曲面圖形的面積為
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(陰影部分)。
(1)設(shè)直線
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與拋物線
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交于兩點
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,且
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,直線
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的斜率為
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,試用
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表示
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;
(2)求
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的最小值。
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(1)可得點
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,設(shè)直線
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的方程為
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直線
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與拋物線
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交于兩點
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,由
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,得
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,∴
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,
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,又
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,
∴
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.
(2)所求的面積:
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=
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=
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=
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=
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令
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,則
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,有
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,
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=
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=
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在
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上為單調(diào)遞增函數(shù),∴當(dāng)
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,即
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時,
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有最小值
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.
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科目:高中數(shù)學(xué)
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題型:解答題
如圖,已知橢圓
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的上頂點為
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,離心率為
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,若不過點
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的動直線
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與橢圓
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相交于
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、
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兩點,且
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.
(Ⅰ)求橢圓
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的方程;
(Ⅱ)求證:直線
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過定點,并求出該定點
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的坐標(biāo).
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科目:高中數(shù)學(xué)
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若橢圓上存在一點P,使得點P到兩焦點的距離之比為
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,則此橢圓離心率的取值范圍是( )
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科目:高中數(shù)學(xué)
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(滿分14分)已知橢圓
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的右焦點
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與拋物線
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的焦點重合,橢圓
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與拋物線
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在第一象限的交點為
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,

,求橢圓
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的方程。
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科目:高中數(shù)學(xué)
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已知點
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動點
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滿足
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,當(dāng)點
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的縱坐標(biāo)為
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時,點
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到坐標(biāo)原點的距離為
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雙曲線
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的一個焦點為

,則
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的值為___________,雙曲線的漸近線方程為___________.
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設(shè)直線
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與橢圓
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相交于
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兩個不同的點.
(1)求實數(shù)
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的取值范圍;
(2)當(dāng)
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時,求
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知
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分別為橢圓
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的左、右兩個焦點,一條直線
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經(jīng)過點
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與橢圓交于
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兩點, 且
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的周長為8。
(1)求實數(shù)

的值;
(2)若
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的傾斜角為
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,求
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的值。
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科目:高中數(shù)學(xué)
來源:不詳
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橢圓

有公共的焦點F
1,F(xiàn)
2,P是兩曲線的一個交點,則
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=( )
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