名校
解题方法
1 . 已知双曲线
:
的左、右焦点分别为
,
,且
,
的一条渐近线与直线
:
垂直.
(1)求
的标准方程;
(2)点
为
上一动点,直线
,
分别交
于不同的两点
,
(均异于点
),且
,
,问:
是否为定值?若为定值,求出该定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.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/1d4f7e7f33963df24d6a46067b4677e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb60dd65c10abde3ba0e4a60132d34d9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b67528f875a6d4bac8bbf784f7b66a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183b6a0cef4256c9696a5bca31053da5.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8828dc0755185a55f816ef1253fcc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bed38b0be75054d5b868b204a88f8ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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12卷引用:陕西省西安市西北工业大学附属中学2023-2024学年高二上学期期中质量检测数学试题
陕西省西安市西北工业大学附属中学2023-2024学年高二上学期期中质量检测数学试题重庆市万州第三中学2023届高三5月模拟数学试题辽宁省抚顺德才高级中学2023届高三下学期硬核提分(七)数学试题(已下线)考点19 解析几何中的探索性问题 2024届高考数学考点总动员【练】(已下线)专题12双曲线(3个知识点5个拓展2个突破8种题型5个易错点)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(人教A版2019选修第一册)江西省赣州市南康中学2024届高三上学期七省联考考前数学猜题卷(七)(已下线)第3章:圆锥曲线与方程章末重点题型复习-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)广东省深圳市深圳外国语学校2024届高三上学期第一次调研数学试题(已下线)模块七 圆锥曲线(测试)(已下线)2.3.1 双曲线的标准方程(十二大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)(已下线)题型24 5类圆锥曲线大题综合解题技巧(已下线)专题8.3 双曲线综合【九大题型】(举一反三)(新高考专用)-2
2 . 设双曲线
,直线
与双曲线
的右支交于点
,
,则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fcd560996764805b57994a97c26e56e.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.双曲线![]() |
B.离心率最小时双曲线![]() ![]() |
C.若直线![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
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6卷引用:陕西省渭南市大荔县2023-2024学年高二上学期期中数学试题
名校
解题方法
3 . 已知双曲线
的右焦点为
,渐近线方程为
.
(1)求双曲线
的方程.
(2)已知双曲线
的左、右顶点分别为
,直线
与双曲线
的左、右支分别交于点
(异于点
),设直线
的斜率分别为
,若点
)在双曲线
上,证明
为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4adb8cdd0c182aaa53ef7a63a97d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63f162c4846a76cadee56ae2f42e37c.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e4d7503a7d57ba242ad4e05c7006a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94bcd25c7dc008c9ec23f6204ad5a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
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6卷引用:陕西省部分学校2024届高三上学期期中联考数学(文)试题
名校
解题方法
4 . 已知双曲线
的左、右顶点分别是
,直线
与
交于
两点(不与
重合),设直线
的斜率分别为
,且
.
(1)判断直线
是否过
轴上的定点.若过,求出该定点;若不过,请说明理由.
(2)若
分别在第一和第四象限内,证明:直线
与
的交点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b30352c43707c4e54b94ce5b61f2e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29dd91ef1fd4c744e89c83b0a6a58152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595ba5dc88bf92a4d6a32b81ca103f03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41441b3d2da6447c7545bd8c11821141.png)
(1)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe61d39d080872caa8973a70a3b4955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a439c8a01a6626d7a3f53af31ef0bcae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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3卷引用:陕西省西安市第一中学等校2023-2024学年高三下学期4月阶段性测试文科数学试题
解题方法
5 . 已知双曲线C:
的右顶点为
,且双曲线C的一条渐近线恰好与直线
垂直.
(1)求双曲线C的方程
(2)若直线
:
与双曲线C的右支交于A,B两点,点F为双曲线C的右焦点,点D在双曲线C上,且
轴.求证:直线
过点F.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb374fd349306abf2f784b6a28d93a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b979396a703fb14715ba39232f5786a.png)
(1)求双曲线C的方程
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303094682b317daea83be885d1c7ff4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5d3a0273d1f3046dfad2086d0df56c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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2023-11-26更新
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3卷引用:陕西省咸阳市礼泉县2023-2024学年高二上学期期中学科素养调研数学试题
名校
解题方法
6 . 已知点
为双曲线
上任意一点,
、
为其左、右焦点,
为坐标原点.过点
向双曲线两渐近线作垂线,设垂足分别为
、
,则下列所述错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.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/1dde8112e8eb968fd042418dd632759e.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
A.![]() |
B.![]() ![]() ![]() ![]() |
C.![]() ![]() |
D.存在点![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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5卷引用:陕西省榆林市第二中学2022-2023学年高二上学期10月期中考试数学(理)试题
陕西省榆林市第二中学2022-2023学年高二上学期10月期中考试数学(理)试题安徽省蒙城一中、涡阳一中等五校2022届高三下学期第二次联考理科数学试题河南省许昌市建安区第三高级中学2022-2023学年高三上学期诊断性测试(二)理科数学试题(已下线)3.3(附加3)圆锥曲线定点与定值问题-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)广东省普宁市华美实验学校2022-2023学年高二下学期第一次月考数学试题
名校
解题方法
7 . 已知双曲线
,过点
的直线l与该双曲线的两支分别交于
两点,设
,
.
(1)若
,点O为坐标原点,当
时,求
的值;
(2)设直线l与y轴交于点E,
,
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257daacf4f9e51faf431d5da4bccd6f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f251dc986252e8b88469aa76bbfe8d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94165c5047e68e952df7a8dc6dc32fda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8968103ac7f02c521e7c3130b9a54f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/112340e2528eb73480721b0f208419b8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70924f16a22ff64187035a74e696b97f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be43c33ac26bcd6559cc320e45d70fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37474e3311493c2e3de8ca62ffc05b64.png)
(2)设直线l与y轴交于点E,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2830a108bfa2a11cb6ea5df1df8b8e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54883e5b7ebfa066c87e1d1d3bd9d65b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff141a77e796894f84d0104f8f947e8a.png)
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2022-10-21更新
|
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9卷引用:陕西省宝鸡市长岭中学2023-2024学年高二上学期期中考试数学试题
陕西省宝鸡市长岭中学2023-2024学年高二上学期期中考试数学试题辽宁省铁岭市昌图县第一高级中学2022-2023学年高二上学期期中数学试题江西省遂川县唐彩高级中学、永丰县欧阳修高级中学2023-2024学年高二下学期第二次联考数学试题河南省豫北名校2022-2023学年高二上学期10月教学质量检测数学试题(已下线)专题15 圆锥曲线大题专项练习(已下线)专题15 圆锥曲线大题专项练习广西北海市2022-2023学年高二上学期期末教学质量检测数学试题江西省南昌市八一中学2022-2023学年高二上学期12月月考数学试题(已下线)专题08 椭圆双曲线综合大题(9题型)-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)
8 . 已知在平面直角坐标系
中,动点
到定点
的距离与到定直线
的距离的比等于常数2.
(1)求动点
的轨迹
的方程;
(2)若直线
与曲线
的另一个交点为
,以
为直径的圆交直线
于
两点,设劣弧
所对的圆心角为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63309dbc3612815f6dbdee23d9a10adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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|
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4卷引用:陕西省咸阳市武功县普集高级中学2022-2023学年高三上学期11月阶段性检测理科重点班数学试题
陕西省咸阳市武功县普集高级中学2022-2023学年高三上学期11月阶段性检测理科重点班数学试题湖南省常德市2021届高三下学期一模数学试题(已下线)2.3 双曲线(提高练)-2021-2022学年高二数学同步训练精选新题汇编(人教A版选修2-1)(已下线)3.2.1 (整合练)双曲线及其标准方程-2021-2022学年高二数学考点同步解读与训练(人教A版2019选择性必修第一册)
解题方法
9 . 已知双曲线的中心在原点,对称轴为坐标轴,一条渐近线方程为
,右焦点
,双曲线的实轴为
,
为双曲线上一点(不同于
,
),直线
,
分别与直线
交于
,
两点.
(1)求双曲线的方程.
(2)证明
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73ac1756e6cc3266bd7198a024f871af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e76582bf1db6ee97233eb508ca37b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](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/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc48974114e23f5a801843710c7ae21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5abb0ff04d2135ceeadc98a850ad38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求双曲线的方程.
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238469e628fb2c454f176be31552cd0c.png)
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