名校
解题方法
1 . 已知双曲线的渐近线方程为
,焦点到渐近线的距离为
,过点
作直线
(不与
轴重合)与双曲线
相交于
两点,过点
作直线
的垂线
为垂足.
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2024-02-10更新
|
477次组卷
|
2卷引用:浙江省杭州高级中学2023-2024学年高二上学期期末考试数学试题
名校
解题方法
2 . 在平面直角坐标系
中,已知
,若动点
满足
则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dfb1d7c122493360e202a56e63e1a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c62ea83bb282ed1793d56b8244f81ada.png)
A.存在点![]() ![]() |
B.![]() ![]() |
C.对任意的点![]() ![]() |
D.椭圆上存在![]() ![]() ![]() ![]() |
您最近一年使用:0次
解题方法
3 . 已知
为椭圆
上的动点,直线
与圆
相切,切点
恰为线段
的中点,当直线
斜率存在时点
的横坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d12ebd10f6c0bcf98be52c32b107f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92395d22b152616800859307113fb58c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
4 . 已知双曲线
,直线
为其中一条渐近线,
为双曲线的右顶点,过
作
轴的垂线,交
于点
,再过
作
轴的垂线交双曲线右支于点
,重复刚才的操作得到
,记
.
(1)求
的通项公式;
(2)过
作双曲线的切线分别交双曲线两条渐近线于
,记
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be56ac444cd8deb01180432555c86b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b293b8d25590ef6f6ae0e9e7486a32a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2214909d55698044e2d16019d902a79.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac2b5502151b6c1e7e3ffe3b8c8988fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7987d2fc837254192070e6a979aa00a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32abe6c3ae6253b064f5e68c2a52bfb.png)
您最近一年使用:0次
2024-02-06更新
|
701次组卷
|
2卷引用:浙江省舟山市2023-2024学年高二上学期期末检测数学试题
5 . 已知动点M到点
的距离与到直线l:
的距离之比等于
.
(1)求动点M的轨迹W的方程;
(2)过直线l上的一点P作轨迹W的两条切线,切点分别为A,B,且
,
①求点P的坐标;
②求
的角平分线与x轴交点Q的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7422cbdb4ad06d155abb2ccdb25ded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求动点M的轨迹W的方程;
(2)过直线l上的一点P作轨迹W的两条切线,切点分别为A,B,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b15b82151bff7cc0238d2034a6129f0.png)
①求点P的坐标;
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
您最近一年使用:0次
解题方法
6 . 已知椭圆
的左右顶点距离为
,离心率为
.
(1)求椭圆
的标准方程;
(2)设过点
,斜率存在且不为0的直线
与椭圆
交于
,
两点,求弦
垂直平分线的纵截距的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be112e60e2e0adcad51a2686ccdc42d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10e8abf8690e4b129466ddb918bcc94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2024-01-31更新
|
972次组卷
|
3卷引用:浙江省湖州市第一中学2024届高三下学期新高考数学模拟试题
名校
解题方法
7 . 已知双曲线
的实轴长为
,直线
交双曲线于
两点,
.
(1)求双曲线
的标准方程;
(2)已知点
,过点
的直线
与双曲线交于
两点,且直线
与直线
的斜率存在,分别记为
.问:是否存在实数
,使得
为定值?若存在,则求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec053f40802aa99a5e4c02f2f0b3fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5a64bcb77f5f64e4af6930c249a270.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3ccc38868099bc4d542e00e0b66685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b312367cf51225ea3bfbee2103b0c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ad58997b9dc0b341c9af08f0cd1fbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c407500c3f3d395fdfdc366851ef3fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2024-01-30更新
|
258次组卷
|
3卷引用:浙江省台州市2023-2024学年高二上学期1月期末质量评估数学试题
8 . 已知焦点在x轴上的椭圆C:,长轴长为4,离心率为
,左焦点为F.点M在椭圆内,且MF⊥x轴,过点M的直线与椭圆交于A、B两点(点B在点A右侧),直线AN、BN分别与椭圆相切且交于点N.
(1)求椭圆的方程;
(2)若直线AF与直线BF的倾斜角互补,则M点与N点纵坐标之积是否为定值,若是,求出定值;若不是,说明理由.
您最近一年使用:0次
2024-01-30更新
|
234次组卷
|
2卷引用:浙江省杭州第二中学2023-2024学年高二上学期期末考试数学试题
名校
解题方法
9 . 已知为抛物线
的顶点,直线
交抛物线于
两点,过点
分别向准线
作垂线,垂足分别为
,则下列说法正确的是( )
A.若直线![]() ![]() ![]() ![]() |
B.若直线![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
2024-01-30更新
|
208次组卷
|
2卷引用:浙江省杭州第二中学2023-2024学年高二上学期期末考试数学试题
10 . 已知双曲线
的左顶点为
,右焦点为F,P为双曲线右支上的点,若双曲线的离心率为2,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25795c321ace603e0466ea05b6d529c.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d386f3691d9b7def0e49b037ff60d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25795c321ace603e0466ea05b6d529c.png)
您最近一年使用:0次