解题方法
1 . 已知双曲线
,直线l与双曲线C的右支交于A,B两点,记
,其中O为坐标原点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4174368661841cb1c9acbce1ddfb57e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c8f7a21d9693033b49c83a66706192.png)
A.m的最小值为2,且此时l与x轴平行 | B.m的最小值为2,且此时l与x轴垂直 |
C.m的最大值为2,且此时l与x轴平行 | D.m的最大值为2,且此时l与x轴垂直 |
您最近一年使用:0次
2021-09-07更新
|
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4卷引用:2017年清华大学THUSSAT附加科目测试数学试题(二测)
2017年清华大学THUSSAT附加科目测试数学试题(二测)湖南省2021届高三下学期高考冲刺试卷(一)数学试题(已下线)考向43 直线与圆锥曲线(已下线)专题13 圆锥曲线-备战2022年高考数学(文)母题题源解密(全国乙卷)
名校
解题方法
2 . 以椭圆
+
=1的顶点为焦点,焦点为顶点的双曲线C,其左、右焦点分别是F1,F2.已知点M的坐标为(2,1),双曲线C上的点P(x0,y0)(x0>0,y0>0)满足
=
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b508366441f805967cdfa5c740d46b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7b938d276e89e287abb64a16ebd989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6500bf4756a6b19a02659473754db916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d1735cbb0931045f86807029b1f758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c512d0f07b1c2e03daabba3fad26433.png)
A.2 | B.4 |
C.1 | D.-1 |
您最近一年使用:0次
2021-01-12更新
|
520次组卷
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5卷引用:【全国百强校】黑龙江省哈尔滨市第六中学2018届高三下学期考前押题卷(二)数学(理)试题
【全国百强校】黑龙江省哈尔滨市第六中学2018届高三下学期考前押题卷(二)数学(理)试题【全国省级联考】湖南湖北八市十二校2019届高三第二次调研联考数学(文)试题(已下线)专题9.4 双曲线 (精练)-2021年高考数学(理)一轮复习学与练(已下线)专题5.2 解析几何与平面向量相结合问题-玩转压轴题,进军满分之2021高考数学选择题填空题河南省周口市周口恒大中学2023-2024学年高二上学期期中数学试题
3 . 对于双曲线
,定义
为其伴随曲线,记双曲线
的左、右顶点为A、B.
(1)当
时,记双曲线
的焦距为
,其伴随曲线
的焦距为
,若
,求双曲线
的渐近线方程;
(2)若双曲线
,弦
轴,记直线PA与QB的交点为M,求动点M的轨迹方程;
(3)过双曲线
的左焦点F且斜率为k的直线l与双曲线
交于
、
两点,证明:对任意的
,在伴随曲线
上总存在点S,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42a960d9c62f797d46caa7a8a4a134a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1f5a9c4d3c70e4b542d7632ae42e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a8ef3f4a8e843a79c3b03adeb61adab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e85963eb36e1406ca2dfd1d039fbeaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0afed911e51011fa097f70d6eec6929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b801ba836652d469036a1d756d808791.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2784a52c4da98dc9df661fc152fc29e.png)
(3)过双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca83a3c2edc7a1d19930fc2dea18b45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7688363f5ffff23a6193c7a8eee501c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5815cc29f60d2aa538c4dd30e0803a4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c96213d5d92b7fdaf1b447921974c4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db28729df26170079075639dd23c1a22.png)
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名校
解题方法
4 . 已知双曲线
的焦点为
,
,其渐近线上横坐标为
的点
满足
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb74c0c2d1e5305cf55cfb9605929268.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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6e29cd72e0bdf6e74bbf27b397fb123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
A.![]() | B.![]() | C.2 | D.4 |
您最近一年使用:0次
2020-11-30更新
|
842次组卷
|
11卷引用:江苏省南通市海安县2020-2021学年高三上学期期中调研考试数学试题
江苏省南通市海安县2020-2021学年高三上学期期中调研考试数学试题江苏省南京市金陵中学、南通市海安中学2020-2021学年高三上学期期中数学试题江苏省南京市第一中学2020-2021学年高三上学期期中数学试题江苏省南通市如皋中学2020-2021学年高二上学期第二次阶段考试数学试题江苏省南通市海安高级中学2020-2021学年高三上学期期中数学试题江苏省盐城市新丰中学2020-2021学年高二上学期期末数学试题苏教版(2019) 选修第一册 必杀技 第三章 3.2.2双曲线的几何性质北师大版(2019) 选修第一册 必杀技 第二章 2.2 双曲线的简单几何性质江苏省常州市教育学会2021-2022学年高二上学期期末学业水平监测数学试题广西桂林市第十八中学2021-2022学年高二下学期开学考试数学(文)试题山东省菏泽市定陶区定陶区明德学校(山大附中实验学校)2022-2023学年高二上学期期中数学试题
5 . 如图,已知双曲线
的方程为
(
),两条渐近线的夹角为
,焦点到渐近线的距离为
.
、
两动点在双曲线
的两条渐近线上,且分别位于第一象限和第四象限,
是直线
与双曲线右支的一个公共点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/77cc1a7a-5595-43f6-9b6f-8c6097c511a7.png?resizew=198)
(1)求双曲线
的方程;
(2)当
时,求
的取值范围;
(3)试用
表示
的面积
,设双曲线
上的点到其焦点的距离的取值范围为集合
,若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b40f995482da39470e40670d6304fcab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3298a22225926e09bd66dbc28a00d05f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/77cc1a7a-5595-43f6-9b6f-8c6097c511a7.png?resizew=198)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6588f0a885efc559eab1e9366bfa5bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0ae951cdae838c492f612e3b9b949.png)
(3)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f02028a3847c4807c2d3cf0ea7efb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41496272c94bf1b0caf3c2d6461c36d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2020-11-15更新
|
579次组卷
|
4卷引用:上海市复旦大学附属中学2020-2021学年高二上学期期中数学试题
上海市复旦大学附属中学2020-2021学年高二上学期期中数学试题(已下线)上海市华东师范大学第二附属中学2021届高三下学期5月高考模拟数学试题上海市实验学校2022-2023学年高二下学期期中数学试题浙江省精诚联盟2022-2023学年高二下学期联考模拟数学试题
名校
解题方法
6 . 对于双曲线
,定义
为其伴随曲线,记双曲线
的左、右顶点为
、
.
(1)当
时,记双曲线
的半焦距为
,其伴随椭圆
的半焦距为
,若
,求双曲线
的渐近线方程;
(2)若双曲线
的方程为
,弦
轴,记直线
与直线
交点为
,求动点
的轨迹方程;
(3)过双曲线
的左焦点
,且斜率为
的直线
与双曲线
交于
、
两点,求证:对任意的
,在伴随曲线
上总存在点
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99cd361ce118bca96a731b241a9c587d.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)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18fde92403135a92e193ad3c7b7439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dad0c75ce33673ec4c425896e8619e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2784a52c4da98dc9df661fc152fc29e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)过双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4058fc45c49e6710ba7e273cb7888704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7688363f5ffff23a6193c7a8eee501c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5815cc29f60d2aa538c4dd30e0803a4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8bf5bb287b1f7f3ad58c862506399a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db28729df26170079075639dd23c1a22.png)
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解题方法
7 . 已知
是双曲线
右支上一点,
分别是双曲线的左、右焦点,
为坐标原点,点
满足
,若
.则以
为圆心,
为半径的圆的面积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f18f176b52ed2f77d94fda9686eee36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7948d32bbe668c180c9cd27beb2e120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c5223d092cbe6952d07fb5a258e6f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
您最近一年使用:0次
名校
解题方法
8 . 已知点
,若
为双曲线
的右焦点,
是该双曲线上且在第一象限的动点,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f429ffba234d522086fd594674ba6cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1fa37c4c826b5dcfebe86ab6177906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a36e853273b9470646caf9ed5442f538.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
9 . 已知双曲线
,
分别为双曲线的左右焦点,
为双曲线
上一点,且位于第一象限,若三角形
为锐角三角形,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0017262e45089093f70001cae2c60257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0d139c9810361b4971904a943856b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5a8e1bc9748e5519dcd9981b7eb251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-06-21更新
|
543次组卷
|
8卷引用:湖北省襄阳五中、夷陵中学、钟祥一中三校2020届高三下学期6月高考适应性考试文科数学试题
名校
解题方法
10 . 已知曲线
,
为曲线
上一动点,过
作两条渐近线的垂线,垂足分别是
和
.
(1)当
运动到
时,求
的值;
(2)设直线
(不与
轴垂直)与曲线
交于
、
两点,与
轴正半轴交于
点,与
轴交于
点,若
,
,且
,求证
为定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a13be757bf0d7dc5940ef18514b56f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/748fb9042744c0d953aa569aa09e59a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0335f0002fca622653e339837e12e47f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73597126975fe452226d8d3473fb100d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d48ccbfe48707e5c53137103b6514d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6096acdd2d0ce16e1e45397ec5e365d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
2020-06-13更新
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798次组卷
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6卷引用:2020届上海市浦东新区高三三模数学试题
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