名校
解题方法
1 . 中心在原点,焦点在坐标轴上,离心率为
,且过点
的椭圆方程是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() |
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2 . 已知椭圆
的右焦点和上顶点分别为点
和点A,直线
交椭圆于P,Q两点,若F恰好为
的重心,则椭圆的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a442ddf58f14997eeb471a80d7959019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3323aea3d92d8c487d6967ac38e58db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-03-06更新
|
1109次组卷
|
4卷引用:浙江省杭州学军中学紫金港校区2023-2024学年高二上学期期中数学试题
3 . 已知
是椭圆和双曲线的公共焦点,
是它们的一个公共点,且
,椭圆的离心率为
,双曲线的离心率为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5918ee27201b342fab2009e7f9d12da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a7bf1e495b950cf39a9146751559c0.png)
A.3 | B.4 | C.5 | D.6 |
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23-24高二上·全国·期中
解题方法
4 . 已知点A,B分别是椭圆的右、上顶点,过椭圆C上一点P向x轴作垂线,垂足恰好为左焦点
,且
,则椭圆C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d1eca88995f1e5606f56cac48e97be0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知右焦点为F的椭圆E:
上的三点A,B,C满足直线AB过坐标原点,若
于点F,且
,则E的离心率是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f2a245381e615882ee5feb7793a1df6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd2fe43cba206f61561a8f92fe53dd9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 已知
分别是椭圆
的左、右焦点,第一象限内的点
在
上,
,直线
的斜率为
,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c6162828793e697cb1ad643b287c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550683c6bd5cee14bcea33bea5764355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab8e57da1a24cba8a5feb1388b2fba6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
7 . 已知矩形
的四个顶点都在椭圆
上,边
和
分别经过椭圆的左、右焦点,且
,则该椭圆的离心率( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56e79f7c3c8815ad1ad3fc8c8d3a50e0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-12-29更新
|
561次组卷
|
2卷引用:安徽省黄山市八校联盟2023-2024学年高二上学期期中考试数学试题
名校
8 . 设
,
分别为椭圆
与双曲线
的公共焦点,它们在第一象限内交于点
,
,若椭圆的离心率
,则双曲线
的离心率
的取值范围为( )
![](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/ff8210484dd6815b5bebc7b22f1389cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d62166e3ab8b16f12c27082d437fdbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74404619ad5699e6c44c947fb569600f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d24a34afd719fd6c20771e1463d3daf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-12-20更新
|
752次组卷
|
5卷引用:江苏省徐州市铜山区2023-2024学年高二上学期学情调研数学试卷
名校
解题方法
9 . 已知右焦点为F的椭圆
上两点A、B,满足直线AB过坐标原点,若
,且
,则E的离心率是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861de3afe17066f65cce25f01b3ef9d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1584b2113456692cd84ef04aceba3ad.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 如图,某同学用两根木条钉成十字架,制成一个椭圆仪.木条中间挖一道槽,在另一活动木条
的P处钻一个小孔,可以容纳笔尖,A,B各在一条槽内移动,可以放松移动以保证
与
的长度不变,当A,B各在一条槽内移动时,P处笔尖就画出一个椭圆E.已知
,且P在右顶点时,B恰好在O点,则E的离心率为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/64fffd5b-6e68-4936-a116-a1f989511b0a.png?resizew=177)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da035673ef0edcfae6b72fb5e5ba34a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e61620a272dada8d4b9a9fab6379dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108a30042e37f9134f9f165c8415c0bb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/64fffd5b-6e68-4936-a116-a1f989511b0a.png?resizew=177)
A.![]() | B.![]() | C.![]() | D.![]() |
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