頂點在原點,以

軸為對稱軸且經(jīng)過點

的拋物線的標準方程為___________.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
.本小題滿分15分)
如圖,已知橢圓
E:


,焦點為

、

,雙曲線
G:


的頂點是該橢

圓的焦點,設(shè)

是雙曲線
G上異于頂點的任一點,直線

、

與橢圓的交點分別為
A、
B和
C、
D,已知三角形

的周長等于

,橢圓四個頂點組成的菱形的面積為

.

(1)求橢圓
E與雙曲線
G的方程;
(2)設(shè)直線

、

的斜率分別為

和

,探求

和


的關(guān)系;
(3)是否存在常數(shù)

,使得

恒成立?
若存在,試求出

的值;若不存在, 請說明理由.
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
平面區(qū)域

是由雙曲線

的兩條漸近線和拋物線

的準線所圍
成的三角形(含邊界與內(nèi)部).若點

,則目標函數(shù)

的最大值為( )
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知

是橢圓

的左、右焦點,過點

作
傾斜角為

的直線

交橢圓于

兩點,

.
(1)求橢圓的離心率;
(2)若

,求橢圓的標準方程.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本題10分)已知拋物線C:

,過原點O作拋物線C的切線

使切點P在第一象限,
(1)求k的值;
(2)過點P作切線的垂線,求它與拋物線C的另一個交點Q的坐標。
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
設(shè)橢圓

的焦點在

軸上,

,

,則這樣的橢圓個數(shù)共有 ( )

、

、

、

、

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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本小題滿分13分)
已知橢圓

:


上的一動點

到右焦點的最短距離為

,且右焦點到右準線的距離等于短半軸的長.
(Ⅰ) 求橢圓

的方程;
(Ⅱ) 過點

(

,

)的動直線

交橢圓

于
、
兩點,試問:在坐標平面上是否存在一個定點

,使得無論

如何轉(zhuǎn)動,以


為直徑的圓恒過定點

?若存在,求出點

的坐標;若不存在,請說明理由.
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科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
不論

如何變化,方程

,都表示頂點在同一曲線上的拋物線,該曲線的方程為______________________
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科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
已知雙曲線

的左、右焦點分別為

、

,拋物線

的頂點在原點,它的準線與雙曲線

的左準線重合,若雙曲線

與拋物線

的交點

滿足

,則雙曲線

的離心率為
.
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