1 . 已知椭圆
的离心率为
,且过点
.圆
的切线l与椭圆E相交于A,B两点.
(2)直线OA,OB的斜率存在为
,
,直线l的斜率存在为k,若
,求直线l的方程;
(3)直线OA,OB与圆
的另一个交点分别为C,D,求
与
的面积之和的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80991c1f0c963104740e50cfff6f29a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b33328faae2d2d4921900e97424de5.png)
(2)直线OA,OB的斜率存在为
![](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/5a08a512b63d60ae9ef4315ed8615542.png)
(3)直线OA,OB与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b33328faae2d2d4921900e97424de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4807ca16360c0cca436e59d4be98f626.png)
您最近一年使用:0次
2024-06-01更新
|
513次组卷
|
3卷引用:【北京专用】高二下学期期末模拟测试B卷
名校
解题方法
2 . 已知椭圆
:
的短轴长为
,且椭圆
经过点
.
(1)求椭圆
的方程;
(2)若过点
的直线与椭圆
相交于
,
两点,且
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7950b79b4e43d650ca5d84e9fce65540.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23baf026a1dd9532845c195a428d8e76.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7df99fe6438442a9453fc0c57fb703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2024-04-07更新
|
645次组卷
|
3卷引用:河南省洛阳市2023-2024学年高二上学期期末考试数学试题
名校
解题方法
3 . 已知点
,
是圆
:
上的任意一点,线段
的垂直平分线交
于点
,设动点
的轨迹曲线为
;
(1)求曲线
的方程;
(2)过点
作斜率不为0的直线
交曲线
于
两点,交直线
于
.过点
作
轴的垂线,垂足为
,直线
交
轴于
点,直线
交
轴于
点,求线段
中点M的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daec826bcf98e738a52fa34eb8a5e85b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8607b7bdbcb604e6fcfbccb66ed2f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fcb20a6972108871adbf284f9e5006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ffda0c209f06e21770aeab0abc8cbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.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/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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2024-04-06更新
|
249次组卷
|
2卷引用:福建省福州市八县(市、区)一中2023-2024学年高二上学期期末联考数学试题
4 . 法国著名数学家蒙日首先发现椭圆两条互相垂直的切线的交点轨迹是以椭圆的中心为圆心的圆,后来这个圆被称为蒙日圆.已知椭圆
,其蒙日圆为圆
,过直线
上一点
作圆
的两条切线,切点分别为
,
,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0296bd9900adcc311f59ad44e940b86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5609d2ccc24a7ab59fdbf8d033227f76.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.圆![]() ![]() | B.四边形![]() |
C.![]() ![]() | D.当点![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
5 . 已知椭圆
的上顶点为
,直线
与椭圆
交于
两点,且直线
与
的斜率之积为
.
(1)求椭圆
的方程;
(2)若直线
,直线
与椭圆
交于
两点,且直线
与
的斜率之和为1,求
与
之间距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b1fb09b447a2a1d6e9e4702d695b3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3016baf1a9ce777f16ea9ce469b2510.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/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5971c1711b7e700586cb045a7eba0b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.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/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2024-03-21更新
|
1279次组卷
|
4卷引用:高二数学下学期期末押题试卷02(测试范围:新高考全部内容)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(新高考专用)
(已下线)高二数学下学期期末押题试卷02(测试范围:新高考全部内容)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(新高考专用)河北省沧州市泊头市联考2024届高三下学期高考模拟考试数学试题河北省张家口市2024届高三一模数学试题江苏省无锡市锡东高级中学2024届高三下学期4月月考数学试题
解题方法
6 . 已知椭圆
过点
,左焦点为
.设直线
与椭圆C交于A,B两点,点M为椭圆C外一点,直线AM,BM分别与椭圆C交于点C,D(异于点A,B),直线AD,BC交于点N.下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87609b100b8d39b52e25ef1bee9b772.png)
A.椭圆C方程为![]() | B.![]() |
C.M,N,O共线 | D.直线MN的斜率为定值![]() |
您最近一年使用:0次
7 . 抛物线C:
,椭圆M:
,
.
(1)若抛物线C与椭圆M无公共点,求实数r的取值范围;
(2)过抛物线上点
作椭圆M的两条切线分别交抛物线C于点P,Q,当
时,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e61e0a1bc2ab34fe0cd1de9f59b0e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181820d1a015068701cfdbdf48b24c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
(1)若抛物线C与椭圆M无公共点,求实数r的取值范围;
(2)过抛物线上点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8adb3358f321cc2c429b9c20674b271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b38040230a7f5674f13c690e780ade.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
您最近一年使用:0次
解题方法
8 . 已知椭圆具有如下光学性质:从椭圆的一个焦点发出的光线射向椭圆上任一点,经椭圆反射后必经过另一个焦点.若从椭圆
的左焦点
发出的光线,经过两次反射之后回到点
,光线经过的路程为8,椭圆C的离心率为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/5/56b2e7d6-e769-41f7-8910-7ab67e254448.png?resizew=204)
(1)求椭圆C的标准方程;
(2)如图,若椭圆C的右顶点为A,上顶点为B,动直线l交椭圆C于P、Q两点,且始终满足
,作
交
于点M,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/5/56b2e7d6-e769-41f7-8910-7ab67e254448.png?resizew=204)
(1)求椭圆C的标准方程;
(2)如图,若椭圆C的右顶点为A,上顶点为B,动直线l交椭圆C于P、Q两点,且始终满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7df99fe6438442a9453fc0c57fb703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bf966a08ed9b4d48deeb2d2b7f24461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7787dfab61ed9830b531da365e592bbd.png)
您最近一年使用:0次
名校
9 . 在平面直角坐标系
中,P为椭圆C:
上的动点,Q为直线l:
上的动点,且
.则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf6dba18751d6641f9fa02f5756be97a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcaada7649455fbebcdbdbb9a94e6a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3de67f64270935ceb31a169d5c8a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638516a8a853dcc41be75f1fcbb73ef1.png)
您最近一年使用:0次
10 . 已知圆
,直线
与圆M交于C,D两点,则下列结论正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/197bed6b6083b62dc2b61ec1ead079ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee66e94d44e2b3dc4d71cd181637e558.png)
A.![]() ![]() |
B.若直线l经过圆M的圆心,则![]() ![]() |
C.当直线l过原点O时,圆M上的动点到直线l的最大距离为![]() |
D.若![]() ![]() |
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