名校
1 . 如图,已知
分别是双曲线
的左、右焦点,过点
的直线与双曲线C的左支交于点A,B,若
则双曲线C的渐近线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48932773034bb6e1651acf140d47822c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7893c7403a17f8ae296fb68fa7bbb92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a30de57df4e6f60bffe9ac591b24fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f36888a9a53591daf619e686d9dc6b0.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-02-05更新
|
291次组卷
|
6卷引用:河南省信阳市固始县2023-2024学年高二上学期期末考试数学试卷
解题方法
2 . 已知双曲线
的一条渐近线方程为
,且经过点
,则C的实轴长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f7fbfa2214ca72495a993b2fed8b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643b31966f52a03f001f2e613cd701dc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 若方程
表示双曲线,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39c6e84907c8fb984f8c0e52a947d61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-02-04更新
|
473次组卷
|
4卷引用:河南省郑州市第十八中学2023-2024学年高二上学期期末模拟数学试题(六)
河南省郑州市第十八中学2023-2024学年高二上学期期末模拟数学试题(六)黑龙江省哈尔滨市六校2023-2024学年高二上学期1月期末联考数学试题山东省烟台市爱华高级中学2023-2024学年高二上学期期末模拟数学试题(二)A卷(已下线)3.2.1 双曲线及其标准方程【第一练】“上好三节课,做好三套题“高中数学素养晋级之路
名校
解题方法
4 . 已知双曲线
,点
,
分别在两条渐近线上(不与原点
重合),点
是
上的一个动点,且
,记直线
的斜率分别为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538724a2186d3433efeceb10e7f7b2d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef7d76b595a30a00dade6f3e1496e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416f71ce7c4353b22d83d04430e5b2b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098e62161dffbcefd4cfdcee73b0a64b.png)
A.![]() | B.当![]() ![]() |
C.![]() | D.![]() |
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5 . 已知函数
,
(
为自然对数的底数),
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2614fa722b7b01b8ad870d7a002c29d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d1660df9815ffb7eba48f2d1e4c399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78d7faf899053d46cc2cb6d4a21e4436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17fcedd0ad93a8827d55fd09007beb30.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
6 . 已知双曲线
:
(
,
)的离心率为2,右焦点
(
)到直线
:
的距离为5.
(1)求
的方程;
(2)设过点
的直线与
的右支交于
,
两点,线段
的垂直平分线分别交直线
和
于点
,
(异于点
),证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24550b13dbecf7d86c7054250e987274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc65bd93cb8a2660f538e97a0a8bfdd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f0c1cdc582622521ff09c30ab919b.png)
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7 . 过抛物线
:
的焦点
的直线交
于
,
两点,若
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d609cb7f8b4d79e8b65c0b8a0672d240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed50b587442312d10eaad5b163ad27ac.png)
A.![]() | B.直线![]() ![]() |
C.以线段![]() ![]() | D.![]() ![]() ![]() |
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解题方法
8 . 已知椭圆
:
(
)的长轴长为10,离心率为
.
(1)求
的方程;
(2)若
的左焦点为
,直线
:
与
交于
,
两点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b7bf464bb7e41f1bddb74180a4fca67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
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9 . 已知点
为动直线
:
所过的定点,若椭圆
截直线
所得的弦被点
平分,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/339843ae6e003375efe26655bd7e10e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4fcce9a9f82de32329294ccdb8c329b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
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10 . 反比例函数
(
)的图像可以看作是由等轴双曲线经过旋转得到的,那么双曲线
的焦距为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef854dfcbba9b7dedc1bc52f6332b011.png)
A.![]() | B.![]() | C.4 | D.6 |
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