1 . 如图,已知双曲线
,过
向双曲线
作两条切线,切点分别为
,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/ecb20051-2b91-4c97-9bd8-5800eec92b84.png?resizew=206)
(1)证明:直线
的方程为
.
(2)设
为双曲线
的左焦点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d750ac23802aa73c47a1528227207485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c9708ef0dc6d6f5dcf6596d3e4f6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/b0a9d9d11c4aff0ff6def84811c07f06.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/ecb20051-2b91-4c97-9bd8-5800eec92b84.png?resizew=206)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e86c6aaaf80865f372891d92a2b7a5b.png)
(2)设
![](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/5cf2fee66accf33325bc1e2f940f8916.png)
您最近一年使用:0次
2022-01-24更新
|
2651次组卷
|
12卷引用:广东省湛江市2021-2022学年高二上学期期末数学试题
广东省湛江市2021-2022学年高二上学期期末数学试题贵州省遵义市2021-2022学年高二上学期期末考试数学(理)试题(已下线)高二上学期期末【常考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)安徽省滁州市定远县民族中学2022-2023学年高二上学期期末数学试题山东省部分学校联考(烟台市第二中学等校)2021-2022学年高三上学期阶段质量检测数学试题河北省石家庄市行唐县2022届高三上学期期末数学试题河北省邯郸市十校联考2022届高三上学期期末数学试题青海省海东市2022届高考一模数学(理)试题(已下线)专题14 圆锥曲线切线方程 微点3 圆锥曲线切线方程综合训练河北省秦皇岛市青龙满族自治县实验中学2023届高三上学期期末数学试题(已下线)考点20 常用的二级结论的应用 2024届高考数学考点总动员(已下线)大招15直线夹角的计算方法
2 . 已知双曲线
:
与椭圆
有公共焦点,
的左、右焦点分别为
,
,且经过点
,则下列说法正确的是( )
![](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/d80b861ba40387cb2bcd04945f5a371a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/de6140983d54ff07307ec65bddd7320e.png)
A.双曲线![]() ![]() |
B.若直线![]() ![]() ![]() |
C.设![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.若动直线![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2021-11-06更新
|
3320次组卷
|
8卷引用:广东省湛江第一中学2023-2024学年高二上学期第二次大考数学试题
名校
3 . 对于无穷数列
,“若存在
,必有
”,则称数列
具有
性质.
(1)若数列
满足
,判断数列
是否具有
性质?是否具有
性质?
(2)对于无穷数列
,设
,求证:若数列
具有
性质,则
必为有限集;
(3)已知
是各项均为正整数的数列,且
既具有
性质,又具有
性质,是否存在正整数
,
,使得
,
,
,…,
,…成等差数列.若存在,请加以证明;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3cb1321c970c49c9f6a5635ac23d6a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99699ac8106034f647e4f460b3bf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa8264eb8eea3025a152318df8720b1.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e836ef3b31693dcaf25b414277e8ae8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d8f894492a8126f5f133dec4cd68833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c414a10d73f453fc1109e5b2243d2369.png)
(2)对于无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926b0a2429ebf269f7e9368ac0306956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e691589e9aafddefcbb613c7030f89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bea0dd7e474bcd04db2544427ba0488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7470297de40027847c5c73fc5d1719c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7334c46af837676ada9575630a48d60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0699adb388000a87241d6b113e733cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969293569368540b9517380795cb571b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bfaf6fb5cd9a53f7adc324976735b9a.png)
您最近一年使用:0次
2019-06-18更新
|
1788次组卷
|
5卷引用:广东省湛江市雷州市第二中学2023-2024学年高二下学期开学考试数学试题
广东省湛江市雷州市第二中学2023-2024学年高二下学期开学考试数学试题2019年上海市普陀区高三高考三模数学试题江西省吉安市第一中学2024届高三“九省联考”考后适应性测试数学试题(一)(已下线)新题型01 新高考新结构二十一大考点汇总-3(已下线)专题06 数列
名校
4 . 数列
满足
,则数列
的前60项和为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0917296e0d73ad1df1b85b6e2f4d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2018-12-20更新
|
1633次组卷
|
2卷引用:【全国百强校】广东省湛江第一中学2018-2019学年高二上学期第二次大考数学(理)试题(B卷)
名校
5 . 已知函数
.
(Ⅰ)当
时,求函数
的极值;
(Ⅱ)讨论
的单调性;
(Ⅲ)若对任意的
,恒有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18d358027300f1ea2952904c2c990ae.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(Ⅱ)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(Ⅲ)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5635c0a80cbdd51c5f48e10bc9c50f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79e15d12d0ce8f0480424d4923b8841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
6 . 已知函数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41db9289a4bd579629e91945dd5d59fe.png)
(Ⅰ)若函数存在单调递减区间,求实数
的取值范围;
(Ⅱ)若,证明:
,总有
.
您最近一年使用:0次
2018-11-15更新
|
1077次组卷
|
2卷引用:【全国百强校】广东省湛江第一中学2017-2018学年高二下学期期中考试数学(理)试题
名校
解题方法
7 . 在平面直角坐标系
中,已知椭圆
的离心率为
,且椭圆
的短轴恰好是圆
的一条直径.
(1)求椭圆
的方程;
(2)设
分别是椭圆
的左,右顶点,点
是椭圆
上不同于
的任意点,是否存在直线
,使直线
交直线
于点
,且满足
,若存在,求实数
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe2c533dbc23a34518f72f3cb14f330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.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/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba9d9fcaa6e7fc5b2da6e7db096205a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2018-08-09更新
|
1439次组卷
|
2卷引用:【全国百强校】广东省湛江第一中学2018-2019学年高二上学期第二次大考数学(理)试题
12-13高二上·广东湛江·期末
8 . 已知椭圆
经过点
,O为坐标原点,平行于OM的直线l在y轴上的截距为
.
(1)当
时,判断直线l与椭圆的位置关系(写出结论,不需证明);
(2)当
时,P为椭圆上的动点,求点P到直线l距离的最小值;
(3)如图,当l交椭圆于A、B两个不同点时,求证:直线MA、MB与x轴始终围成一个等腰三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a667af488582538fc08d8e454d5543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0bea681006f614f8a070e9c6a942c04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41b8856f1acaf13e6968f0a96f37795.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f7bc699f2bf19dd5a7635375cd3c8e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f7bc699f2bf19dd5a7635375cd3c8e.png)
(3)如图,当l交椭圆于A、B两个不同点时,求证:直线MA、MB与x轴始终围成一个等腰三角形.
![](https://img.xkw.com/dksih/QBM/2012/1/16/1570692813488128/1570692819148800/STEM/c8ea6302-eb33-4b32-834e-0c3f11680e2c.png?resizew=221)
您最近一年使用:0次