解题方法
1 . 已知双曲线C1过点(4,-6)且与双曲线C2:
共渐近线,点Р在双曲线C1上(不包含顶点).
(1)求双曲线C1的标准方程;
(2)记双曲线C1与坐标轴交于A,B两点,求直线PA,PB的斜率之积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c99580b2a33da8968f0f7f86b89492e.png)
(1)求双曲线C1的标准方程;
(2)记双曲线C1与坐标轴交于A,B两点,求直线PA,PB的斜率之积.
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名校
解题方法
2 . 已知双曲线
的右焦点为
,且点
在双曲线C上.
(1)求双曲线C的方程;
(2)过点F的直线与双曲线C的右支交于A,B两点,在x轴上是否存在不与F重合的点P,使得点F到直线PA,PB的距离始终相等?若存在,求出点P的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0504d6aff5ab16cb5eb7352407f945d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b162f1e3128f25b0dfa4bd70e96dfb61.png)
(1)求双曲线C的方程;
(2)过点F的直线与双曲线C的右支交于A,B两点,在x轴上是否存在不与F重合的点P,使得点F到直线PA,PB的距离始终相等?若存在,求出点P的坐标;若不存在,请说明理由.
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2022-12-29更新
|
1349次组卷
|
9卷引用:甘肃省张掖市某重点校2022-2023学年高二下学期5月月考数学试题
甘肃省张掖市某重点校2022-2023学年高二下学期5月月考数学试题广东省部分学校2022-2023学年高三年级12月大联考数学试题湖北省襄阳市第一中学2022-2023学年高二上学期期末数学试题(已下线)专题10 圆锥曲线综合大题10种题型归类-【寒假分层作业】2024年高二数学寒假培优练(人教A版2019选择性必修第一册)专题04 双曲线15种常见考法归类(3)河南省2022-2023年度高三模拟考试数学(文科)试题河南省2023届高三模拟考试理科数学试题辽宁省辽阳市2022-2023学年高三上学期期末数学试题(已下线)专题7-4圆锥曲线五个方程型大题归类-2
名校
解题方法
3 . 已知圆M:
的圆心为M,圆N:
的圆心为N,一动圆与圆N内切,与圆M外切,动圆的圆心E的轨迹为曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d30bb07aa3a594041266cdfdeb42ab.png)
(1)求曲线C的方程;
(2)已知点
,直线l不过P点并与曲线C交于A,B两点,且
,直线l是否过定点?若过定点,求出定点坐标;若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3f96231c15b003adeccf8b05fff07c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac870e89808bf58d955eca4ff13aef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d30bb07aa3a594041266cdfdeb42ab.png)
(1)求曲线C的方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87c89f4cafedc9cb6a0236f4d4bb7f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b768ea6a05cbf45b28fc46c501ba532.png)
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2022-12-28更新
|
769次组卷
|
9卷引用:湖北省黄冈市黄梅县国际育才高级中学2023-2024学年高二上学期12月月考数学试题
湖北省黄冈市黄梅县国际育才高级中学2023-2024学年高二上学期12月月考数学试题广东省深圳市光明区2021-2022学年高二上学期期末数学试题山东省潍坊市潍坊第一中学2021-2022学年高二上学期期末数学试题山东省临沂市莒南第一中学2022-2023学年高二上学期期末数学试题(已下线)高二数学上学期期末模拟试卷01(选择性必修第一册+数列)-【题型分类归纳】2022-2023学年高二数学同步讲与练(人教A版2019选择性必修第二册)(已下线)高二上学期期末【压轴60题考点专练】(选修一+选修二)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)湖南省永州市祁阳县第四中学2023-2024学年高二上学期期中数学试题江苏省镇江市镇江中学2022-2023学年高二上学期期末数学试题(已下线)第09讲 高考难点突破一:圆锥曲线的综合问题(定点问题) (精讲)-1
4 . 在平面直角坐标系
中,动点M到点
的距离等于点M到直线
的距离的
倍,记动点M的轨迹为曲线C.
(1)求曲线C的方程;
(2)已知直线
与曲线C交于A,B两点,曲线C上恰有两点P,Q满足
,问
是否为定值?若为定值,请求出该值;若不为定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/269a51e0f77f63bae2df3dc8b1d4f455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
(1)求曲线C的方程;
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94496266250d72d9b89502e3b99549d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e57ec500ea2dd6d2f94b82a0425f0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
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名校
解题方法
5 . 已知
,
,点
满足
,记点
的轨迹为
.
(1)求轨迹
的方程;
(2)斜率为
的直线
过点
,且与轨迹
的右支相交于
两点.求斜率
的取值范围;
(3)在(2)的条件下,在
轴上是否存在定点
,使得无论直线
绕点
怎样转动,总有
成立?如果存在,求出定点
;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813f9a2814013e2407b5b1c216159359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fd15503ee692f8286b0312f7c6f0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d6cd9241b2c3284fa10752c300aba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)斜率为
![](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/a3fb78c5f885034612c0e030b920143d.png)
![](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/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)在(2)的条件下,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada25f76504c3fd1226da43c94cb4277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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6 . 已知曲线
上任意一点
到
的距离是它到
的距离的
倍.
(1)求曲线
的方程;
(2)直线
交x轴于N,与曲线C在第一象限的交点为E,过点N的直线
与曲线C交于F,G两点,与直线
交于点K,记EF,EG,EK的斜率分别为
,
,
,求证:
是
,
的等差中项
![](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/3d599059e6b2c918ab15ee22611b6962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17564fc1858bd4cf74caf2b15607b6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38869aee297ceabce9e41aa0ffdc133c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
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解题方法
7 . 椭圆
的左右焦点分别为
,右顶点为
为椭圆
上任意一点,且
的最大值的取值范围是
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57654bf131df03b31d3d11b5b656c73d.png)
(1)求椭圆
的离心率
的取值范围
(2)设双曲线
以椭圆
的焦点为顶点,顶点为焦点,
是双曲线
在第一象限上任意一点,当
取得最小值时,试问是否存在常数
,使得
恒成立?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e6314e24c0225d455415c52124052b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff571c72c041d8668b4d2754679f64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34005d3b709a89e3db6bb786bbfb2369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad593cdf57ecac6fbe2e42e14cff81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57654bf131df03b31d3d11b5b656c73d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(2)设双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc983f1bad03411ae64d84ff7bdf2551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e0151ba96c13c3637060f9cee498a91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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解题方法
8 . 双曲线
:
的离心率为
,且点
在双曲线
上.
(1)求曲线
的方程;
(2)动点M,N在曲线
上,已知点
,直线PM,PN分别与y轴相交的两点关于原点对称,点
在直线MN上,
,证明:存在定点
,使得
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a147fa7817d3b0cd94cadfb340cf846.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)动点M,N在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de78b493bc2cc9696c584325c22ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7555f635da615b09b7e2f08ddbeaf1db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eebe4d3c925e04eb4a5e0318143482fb.png)
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解题方法
9 . 已知双曲线
的焦距为8,双曲线
的左焦点到渐近线的距离为2.
(1)求双曲线
的方程;
(2)设
分别是双曲线
的左、右顶点,
为双曲线
上任意一点(
不与
重合),线段
的垂直平分线交直线
于点
,交直线
于点
,设点
的横坐标分别为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/782c9e617a2bd1391c2d7a29aec0bb73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48d5ab4cc1d9ec97efa3e78d954be50.png)
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解题方法
10 . 已知双曲线
的右焦点为
,离心率为2,直线
与双曲线
的一条渐近线交于点
,且
.
(1)求双曲线
的标准方程;
(2)设
为双曲线
右支上的一个动点,证明:在x轴上存在定点
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24550b13dbecf7d86c7054250e987274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa5d6092f598c7da4796f965e40525a.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/760f8b8aaedafe2d4e7ecdd2ea752460.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352a208a70e8cc21a8e26cb029574cf4.png)
您最近一年使用:0次