解题方法
1 . 椭圆
的左、右顶点分别为
,点
在椭圆上第一象限内,记
,存在圆
经过点
,且
,则椭圆
的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f04443a0c1cf4808aea741c9f9379b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eeab4cb28085f2fc9f058656e03352c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01225eca2322a6136314dedadcafa994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bde656c56535b611568bdf754986fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2 . 已知直线
与抛物线
相切于点P,过P作两条斜率互为相反数的直线,这两条直线与C的另一个交点分别为A,B,直线
与C交于M,N两点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1ba86ffc6e5542b62319848c14acaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c30fd97fafb3779aa4f4660f41e2939.png)
A.![]() | B.线段AB中点的纵坐标为![]() |
C.直线AB的斜率为![]() | D.直线PM,PN的斜率之积为4 |
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解题方法
3 . 已知椭圆E的中心为坐标原点,对称轴为x轴、y轴,且过点
,
.
(1)求E的方程;
(2)已知
,是否存在过点
的直线l交E于A,B两点,使得直线PA,PB的斜率之和等于
?若存在,求出l的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c1c99171ae3215a2e99a5deb287798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/730fee0ab948dd7011c1cf21619ba07e.png)
(1)求E的方程;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56ab70e602f2e2e291df643ab209162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad434a7febc9d1491e73f51b86cd588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
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2023-05-24更新
|
989次组卷
|
5卷引用:安徽省六安第一中学2023届高考适应性考试数学试题
安徽省六安第一中学2023届高考适应性考试数学试题陕西省安康中学2023届高三下学期5月学业质量检测(二)文科数学试题陕西省安康中学2023届高三下学期5月学业质量检测(二)理科数学试题河北省衡水市第二中学2023届高三三模数学试题(已下线)广东实验中学2024届高三上学期第一次阶段考试数学试题变式题19-22
4 . 已知
为椭圆
:
上两点,点
满足
,过点A与点
的直线与直线
交于点
.
(1)当
轴且A在
轴上方时,求直线
的斜率;
(2)已知
,记
的面积为
,
的面积为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae1567d8f98fabc1a3948f8602cc5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa77802f9a072a800ee5098f668d5d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e4f7a580e6a3352591f0179781d329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4d488d56b95a44a6b0b40d3e89c010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2d6c92ff8a66da502681710445fe99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da322ac8867e8a47c6588601078abf18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24624dffd30b66a5e4de57362b32b2a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d04ad48605ed31fd39fa962c5cccc412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a5e0a51c9e14fb246b0ba0b231c1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
5 . 已知点
,圆C:
,过点F的直线l交圆C于A,B两点,线段AB的中点为
.
(1)求动点
的轨迹Γ方程;
(2)设轨迹Γ与x轴交于D,E两点(点E在点D的右侧),过点D作x轴的垂线m,过点F作直线DP的垂线n,垂线m与n交于点Q,求证:点P,Q,E共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d5a1444054ea168ab3ccd737faa17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c7db7d0205b790f0d09fb813fcaf7fe.png)
(2)设轨迹Γ与x轴交于D,E两点(点E在点D的右侧),过点D作x轴的垂线m,过点F作直线DP的垂线n,垂线m与n交于点Q,求证:点P,Q,E共线.
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6 . 如图,已知椭圆
:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
经过点
,
、
为椭圆的左右顶点,
为椭圆的右焦点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/3/05ac6a57-d91c-4044-915d-57723082f7b5.png?resizew=190)
(1)求椭圆
的方程;
(2)已知经过右焦点
的直线
(不经过点
)交椭圆
于
、
两点,交直线
:
于点
,若
,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f82eb4ba631d0f50d848aa6e576b379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e641014eb998f16c14ee0ec59f9d54f0.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a6c39fe819c4e4d7bd73422790189b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/3/05ac6a57-d91c-4044-915d-57723082f7b5.png?resizew=190)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知经过右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/81dba07103f7202b99145f5015a7b51a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b719544a5fcd5f0347a2a4b0544b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2022-04-14更新
|
585次组卷
|
5卷引用:安徽省黄山市2022届高三下学期第二次质量检测文科数学试题
安徽省黄山市2022届高三下学期第二次质量检测文科数学试题安徽省合肥市肥东县综合高中2021-2022学年高三下学期期中文科数学试题(已下线)回归教材重难点04 圆锥曲线-【查漏补缺】2022年高考数学(文)三轮冲刺过关江西省新余市2023届高三上学期期末质量检测数学(文)试题四川省绵阳南山中学实验学校2023届高考模拟六(文科)数学试题
名校
解题方法
7 . 已知动点M到直线
的距离是M与点
距离的
倍,记M的轨迹为曲线C.
(1)求曲线C的方程;
(2)动直线
与C交于两点A,B,曲线C上是否存在定点P,使得直线
的斜率和为零?若存在求出点P坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a812a9b58ccba331cfd21d244329af01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
(1)求曲线C的方程;
(2)动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2363514688e165d2ebe99b016e51becc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
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2022-02-04更新
|
408次组卷
|
2卷引用:安徽省部分学校2021-2022学年高三上学期期末联考文科数学试题
名校
解题方法
8 . 已知椭圆
:
,其短轴为2,离心率为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/191e6dfd-bf57-44eb-b2e4-4248e55b0351.png?resizew=152)
(1)求椭圆
的方程;
(2)设椭圆
的右焦点为
,过点
作斜率不为0的直线交椭圆
于
,
两点,设直线
和
的斜率为
,
,试判断
是否为定值,若是定值,求出该定值;若不是定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/191e6dfd-bf57-44eb-b2e4-4248e55b0351.png?resizew=152)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8797fc4a235dd9be9e5af539aca37e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2273ae1ee99cec9c1304323bc9ebf75f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1460aa3d83df61f6c411b34412135451.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/b69e3f7ddd51215d00661c09cd900d60.png)
您最近一年使用:0次
2021-07-04更新
|
745次组卷
|
2卷引用:安徽省淮北市2021届高三二模数学(文)试题
9 . 已知点
在圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f94c7b530a908f1792fbd1e9e7c505a.png)
上运动,点
在
轴上的投影为
,动点
满足
.
(1)求动点
的轨迹
的方程;
(2)设
,过点
的动直线
与曲线
交于
(不同于
)两点.问:直线
与
的斜率之比是否为定值?若为定值,求出该定值;若不为定值,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f94c7b530a908f1792fbd1e9e7c505a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08227ca941898eb34941f446ca8b1de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/528611d328610818c6565e48903e07a5.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3aab7d462df3d3f297f3d0fc5e5a75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
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2020-03-21更新
|
1000次组卷
|
5卷引用:安徽省淮北市第一中学2019-2020学年高三下学期第五次考试数学(理)试题
安徽省淮北市第一中学2019-2020学年高三下学期第五次考试数学(理)试题广东省番禺区2020届高三摸底测试文科数学试题2020届金太阳高三4月联考数学(理)试题(已下线)专题06 平面向量在解析几何中的应用(第五篇)-2020高考数学压轴题命题区间探究与突破2020届河南广东等省高三普通高等学校招生全国统一考试4月联考数学(理)试题
10 . 已知函数
在区间
内任取两个实数
,且
,不等式
恒成立,则实数
的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ad74073e637c6c326023e9c062e9a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d14e88b76e8fbfed5a6b57a9e708fc21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f634030f868e861729d0c8b746d108.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2018-11-30更新
|
1342次组卷
|
2卷引用:【市级联考】安徽省黄山市普通高中2019届高三11月“八校联考”数学(理)试题