名校
解题方法
1 . 已知椭圆
过点
,点A为下顶点,且AM的斜率为
.
(1)求椭圆E的方程;
(2)如图,过点
作一条与y轴不重合的直线,该直线交椭圆E于C、D两点,直线AD,AC分别交x轴于H,G两点,O为坐标原点.证明:
为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4b7a89314265c2c84dfacc2d65436b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/19/c3322f2a-d836-4997-b55a-305053d5060b.png?resizew=170)
(1)求椭圆E的方程;
(2)如图,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d429efe96d68065e7d433c996682791d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb69d065b4d9e72fd87efe936fb8211.png)
您最近一年使用:0次
2023-07-14更新
|
758次组卷
|
5卷引用:湖北省孝感市2023-2024学年高二上学期11月期中考试数学试题
名校
解题方法
2 . 已知椭圆
的方程为
,
在椭圆上,离心率
,左、右焦点分别为
、
.
(1)求椭圆
的方程;
(2)若直线
与椭圆
交于
,
两点,连接
,
并延长交椭圆
于
、
两点,连接
,试探索直线
与直线
的斜率之比是否为定值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/082990da1f11a1a7be4fc3935c0d526e.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/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbad65b3d744b70da2480eee1cdb587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
您最近一年使用:0次
2023-05-20更新
|
376次组卷
|
2卷引用:湖北省孝感、荆州部分中学2022-2023年高三下学期5月联考数学试题
名校
解题方法
3 . 已知离心率为
的椭圆
经过点A(2,1).
(1)求椭圆C的方程.
(2)不经过点A且斜率为
的直线
与椭圆C相交于P ,Q两点,若直线AP与直线AQ的斜率之积为
,试问
是否为定值?若是,求出该定值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
(1)求椭圆C的方程.
(2)不经过点A且斜率为
![](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/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2023-05-08更新
|
1238次组卷
|
12卷引用:湖北省孝感市部分学校2022-2023学年高二下学期5月联考数学试题
湖北省孝感市部分学校2022-2023学年高二下学期5月联考数学试题陕西省商洛市2023届高三三模理科数学试题陕西省商洛市2023届高三三模文科数学试题河南省洛阳市创新发展联盟2022-2023学年高二下学期5月月考数学试题辽宁省朝阳市凌源市2022-2023学年高二下学期期中数学试题陕西省商洛市洛南中学2022-2023学年高二下学期6月月考理科数学试题广东省湛江市第二中学2022-2023学年高二下学期第二次月考数学试题云南省曲靖市富源县2022-2023学年高二下学期5月月考数学试题湖南省部分校2022-2023学年高二下学期5月月考数学试题江西省万安中学2022-2023学年高二下学期期中数学试题云南省曲靖市麒麟区曲靖二中云师中学2023-2024学年高二上学期期中数学试题(已下线)专题15 圆锥曲线综合
解题方法
4 . 已知在平面直角坐标系
中,椭圆
的中心在坐标原点,焦点在
轴上,焦距等于
,且经过点
.
(1)求椭圆
的标准方程;
(2)记椭圆
的左、右顶点分别为
,
,点
是椭圆
上位于
轴上方的动点,直线
,
与直线
分别相交于
,
两点,求线段
的长度的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a7a78a0cb55d2396f7213432a86b86.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)记椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.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/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c77e9c89b7275b0c1a9af5c9a72e5968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b5e290c6b2c5508a3bf6117afbf7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccfd9353adb70d7811b938f6b3aa377e.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/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2023-04-15更新
|
364次组卷
|
2卷引用:湖北省孝感市2022-2023学年高二下学期期中联考数学试题
5 . 已知点
为椭圆
上一点,A、B分别为C的左、右顶点,且
的面积为5.
(1)求C的标准方程;
(2)过点
的直线l与C相交于点M,N(点M在x轴上方),
与y轴分别交于点G,H,记
分别为
(点O为坐标原点)的面积,探索
是否为定值并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e09325b1852ea117c1fc43ce9078ad4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e8c7968d57d2a20065a7cb15c9b4eb.png)
(1)求C的标准方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f449cadb49859b80c31ef1f68bfe81b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e4d7503a7d57ba242ad4e05c7006a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa19d2e08ad4b8938796a9971d905d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ad5a9147b25285124851a61c7d1a24a.png)
您最近一年使用:0次