名校
1 . 已知椭圆的方程为
,则它的焦点坐标为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/929070fe8b66d57fcfb19ec2b70218d3.png)
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2 . 在平面直角坐标系
中,椭圆
的左,右焦点分别为
,椭圆
的弦
与
分别平行于
轴与
轴,且相交于点
.已知线段
的长分别为
,则
的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fcb20a6972108871adbf284f9e5006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8d4aa43f4bf9ade4a8fba4e4a29e924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c28f88812282308b664d3bfc276150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffdc208786577c5c51e9ecfb6a8ce2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
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名校
3 . 以椭圆的两个焦点和短轴两个顶点为四个顶点的椭圆方程为
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名校
4 . 已知结论:椭圆
的面积为
.如图,一个平面
斜截一个足够高的圆柱,与圆柱侧面相交的图形为椭圆
.若圆柱底面圆半径为
,平面
与圆柱底面所成的锐二面角大小为
,则下列对椭圆
的描述中,错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b30489cd9c57a2c6283e0fc36129728c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f727d47ac94c374adb4fc3131dcca1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
A.短轴为![]() ![]() | B.离心率为![]() ![]() |
C.焦距为![]() | D.面积为![]() |
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5 . 椭圆
的焦点坐标为 ______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c190e8bb81a4d26cf638ed246193cc9.png)
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解题方法
6 . 根据下列条件,分别求出曲线的标准方程:
(1)焦距是
,过点
,焦点在
轴上的椭圆;
(2)一个焦点是
,一条渐近线方程为
的双曲线;
(3)焦点到准线的距离是
,而且焦点在
轴上的抛物线.
(1)焦距是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b273241821170be56c5251d48386013b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(2)一个焦点是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3eda23a1350120ef959ae541d36657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953b0e963195605a67975c6f8f3caa0c.png)
(3)焦点到准线的距离是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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7 . 已知抛物线
与椭圆
有公共的焦点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
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8 . 离心率
的双曲线与椭圆
有公共焦点,则该双曲线实轴长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf225b4a29dc973d00c0d0dd76b45288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608d1a8669aa2426e12751dec3e96da6.png)
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名校
解题方法
9 . 已知椭圆
,
,
为左、右焦点,直线
过
交椭圆于A、B两点.
(1)求椭圆的焦点坐标和离心率;
(2)若
,求直线
的方程;
(3)若直线
交
轴于
,直线
交
轴于
,是否存在直线
,使
,若存在,求出直线
的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c763113a1fc48e8acc83787b8cd24eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
(1)求椭圆的焦点坐标和离心率;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55a9b3e16e7f56fc5c6a8f46bb60c84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbad65b3d744b70da2480eee1cdb587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6481bdb14db168814440057c358b47b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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名校
10 . 椭圆
的焦距为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d86650634148aa9e4f03660f5d4355.png)
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