名校
1 . 已知双曲线
的左,右焦点分别为
为双曲线
上点,且
的内切圆圆心为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfae4a70f826b242c3d5b6c64c8d8f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ed463bf16c78a4bbb9d3acff922afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1fdbdd6a20cf015cc17a28de359cc.png)
A.![]() | B.直线PF1的斜率为![]() |
C.![]() ![]() | D.![]() ![]() |
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解题方法
2 . 已知双曲线
过点
且渐近线为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e700a11b86a43272db539bc6d97211f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4b54285784578101392a371a5e7040.png)
A.![]() ![]() |
B.![]() ![]() |
C.直线![]() ![]() |
D.![]() ![]() |
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解题方法
3 . 已知双曲线
的左焦点为
,过坐标原点
的直线与双曲线
交于
两点,且点
在第一象限,满足
.若点
在双曲线
上,且
,则双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ed44d86cace7852eaa810b6a554bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babfc8ea7a7cbfbd9c1f8f61bf19a36f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-06-11更新
|
101次组卷
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2卷引用:重庆市巴蜀中学校2024届高三下学期模拟预测数学试卷
名校
解题方法
4 . 已知双曲线C:
的左、右焦点分别为
,
,直线
:
与C的左、右两支分别交于M,N两点(点N在第一象限),点
在直线
上,点Q在直线
上,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c477e5ade921ffa8377c4719319380ff.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/b2c903d79a2e83aa823b212b34915abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa3839129fc7ae89e70d24e3d03694b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a12a030f853a383a50fd889486c9f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5be30af9107107bb6f99bcedfac8c83.png)
A.C的离心率为3 | B.当![]() ![]() |
C.![]() | D.![]() |
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2024-06-10更新
|
529次组卷
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4卷引用:重庆市西南大学附属中学校2024届高三下学期全真模拟集训(四)数学试题
名校
5 . 过双曲线
的右焦点F作与其中一条渐近线垂直的直线
分别与这两条渐近线交于
两点,若
,则该双曲线的焦距为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/222b4c3088d36ba0b2f5d8dedbcfc902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff58702fa978040dc5b2a8a5c19304c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413a0dc5bc9714fc913ee8219005e91e.png)
A.2 | B.3 | C.![]() | D.4 |
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2024-06-10更新
|
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2卷引用:重庆市西南大学附属中学2024届高考全真模拟数学试题
6 . 已知双曲线
的左、右焦点分别为
,点
在双曲线M上,且
.
(1)求双曲线M的方程;
(2)记
的平分线所在的直线为直线l,证明:双曲线M上存在相异两点
关于直线l对称,并求出
(E为
的中点)的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df9fc57543a845650820579d77cf787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acf45a5f66394502b70bf1dd68ee40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d35cbbf27988042e54db08ab9ec5d34.png)
(1)求双曲线M的方程;
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62180fb2b68724b7b0f4f8337496c12a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf265581fcae70808cbcee6af7ec8e99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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解题方法
7 . 已知双曲线C:
,则其离心率可能为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3838345ff69549a344749e3f2f95d2e1.png)
A.2 | B.![]() | C.![]() | D.![]() |
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8 . 已知
是双曲线
的左右顶点,动点
是双曲线上异于
的任意一点,且满足直线
与
的斜率之积为3.
的方程;
(2)已知点
为双曲线
的右焦点,过点
作直线
交双曲线右支于A,B两点,过点
且与直线
垂直的直线
交直线
于点P,O为坐标原点,直线OP交双曲线于M,N两点.设直线
的斜率分别为
,且
.
(i)证明:双曲线
在
点处的切线经过点
;
(ii)记
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02fee8c9e99a3e589f0bceb317752f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e613d549f84fd569652e36a3228a0442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf1c604f7a3a9ffe22e33f399ab4e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知点
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1710916ae846e08a5927dae3ad762342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c65902e35640cf2c8d4111c36b40145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee3e87a46fc97708046c37aa77712db.png)
(i)证明:双曲线
![](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/dad2a36927223bd70f426ba06aea4b45.png)
(ii)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba666787158dec7e8498f106c79879a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca8057293913227c0769495e927e9acb.png)
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解题方法
9 . 双曲线
的焦点为
(
在
下方),虚轴的右端点为
,过点
且垂直于
轴的直线
交双曲线于点
(
在第一象限),与直线
交于点
,记
的周长为
的周长为
.
(1)若
的一条渐近线为
,求
的方程;
(2)已知动直线
与
相切于点
,过点
且与
垂直的直线分别交
轴,
轴于
两点,
为线段
上一点,设
为常数.若
为定值,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f138353ee83b5b04bd639cce32958913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0cedd8765aeb593658ceda8e2f63d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cee208be15b03e13b774ed4e40e05b9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bdeeb6f5e38e3464c357d00839a6ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2970a59f8c60981fce9193c9de18985a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d1484a1c2a3bfac1041835f90034cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2baa39f06afdda719bae35fe7c478324.png)
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2024-05-29更新
|
733次组卷
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3卷引用:重庆市乌江新高考协作体2024届高考模拟监测(二)数学试题
名校
解题方法
10 . 已知M为双曲线C:
上的动点,过点M作C的两条渐近线的垂线,垂足分别为P,Q.
(1)求
的值;
(2)设
,
分别为双曲线C的左、右顶点,过点
的直线l与双曲线C交于A,B两点(点A在x轴上方),R为直线
,
的交点,若点R的纵坐标为
,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dad0c75ce33673ec4c425896e8619e4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751d11a71e1fdf02c4a990220ca4e67d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c3a2f5b0702ea9fbb9dc8904579737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668438e15423368cd744445e824d18a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa585b9257ed0798213a9ae9b87d291.png)
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