19-20高一·浙江杭州·期末
1 . 如图,已知椭圆
,斜率为
的直线
与椭圆
交于
两点,过线段
的中点
作
的垂线交
轴于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/9ac76425-0fdc-4e5e-a362-cfa02e3b988b.png?resizew=230)
(1)设直线
的斜率分别为
,若
,直线
经过椭圆
的左焦点,求
的值;
(2)若
,且
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dc555ee95335fccb1fb911f3d7b2122.png)
![](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/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/9ac76425-0fdc-4e5e-a362-cfa02e3b988b.png?resizew=230)
(1)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a5e484dfef494d27bc35ae7b8cf75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1efe96e7776f1b5dfa92c295f8d97d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cef568cfe2fc12a4dec11533ada274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b199e8fc1ea7f0ffbb95e70993ec72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b8b6cca20cf91402279881af374628.png)
您最近一年使用:0次
2 . 在平面直角坐标系
中,已知椭圆
的四个顶点围成的四边形的面积为
,椭圆的左焦点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45349f54f6abc8d331556557255f024.png)
![](https://img.xkw.com/dksih/QBM/2021/2/3/2650310066290688/2651388766789632/STEM/57d1f4d7646349e9b8f520c315651e03.png?resizew=185)
(1)求椭圆的方程;
(2)
,是否存在斜率为
的直线l与椭圆相交于两点M,N,且
,若存在,求出直线l的方程,若不存在,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/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45349f54f6abc8d331556557255f024.png)
![](https://img.xkw.com/dksih/QBM/2021/2/3/2650310066290688/2651388766789632/STEM/57d1f4d7646349e9b8f520c315651e03.png?resizew=185)
(1)求椭圆的方程;
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9cb4b48bdfbb1aa677e5d8dcc7ad8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b485b62d004d52fb31d6ed99ccb7669.png)
您最近一年使用:0次
解题方法
3 . 设椭圆
的离心率为
,上、下顶点分别为A,B,
.过点
,且斜率为k的直线l与x轴相交于点F,与椭圆相交于C,D两点.
(1)求椭圆的方程;
(2)若
,求k的值;
(3)是否存在实数k,使
?若存在,请求出k的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dfc9d1109fe41145cc892b5702d9fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/887e587a4fb083a37f3d84f42874ec16.png)
(1)求椭圆的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749855e4423d1be916990f7345eeca76.png)
(3)是否存在实数k,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8148607c5d131d1ce7c1d89c1958459e.png)
您最近一年使用:0次
4 . 已知椭圆
的左焦点为F,椭圆外一点
,直线
交椭圆于A、B两点,过P作椭圆C的切线,切点为E,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533b93dd6eb6b474481247736699c76c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985a0a60acd2d254fe6f596912cf9a62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e752a72356fcde45fea0541d5ed2d64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
您最近一年使用:0次
名校
解题方法
5 . 已知椭圆
的离心率为
,右焦点为
.
(
)求椭圆
的方程.
(
)设点
为坐标原点,过点
作直线
与椭圆
交于
,
两点,若
,求直线
的方程.
![](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/95ed2c6c8e93e6ba3737bf4b2aa2b81c.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](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/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/5c0b06dc01c30d13f64be2ac6a1d811e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2018-02-24更新
|
688次组卷
|
5卷引用:江西省景德镇一中2020-2021学年高一(2班)下学期期中考试数学试题
20-21高一·浙江·期末
6 . 已知椭圆
,
、
为左、右焦点,
.
(1)求
及
的角平分线所在直线
的方程;
(2)在椭圆
上是否存在关于直线
对称的相异两点?若存在,请找出:若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a909cfbe59a736f3d2024723dba27c13.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/98b2cc0d2f6d3eee9a33db83e0c0830d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a22060ef445f62db6c9f0d506fe7fd3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62180fb2b68724b7b0f4f8337496c12a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)在椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
7 . 已知椭圆
的离心率为
, 椭圆短轴的一个端点
与两焦点
、
构成的
的面积为
.
(Ⅰ)求椭圆
的方程;
(Ⅱ)设直线
与椭圆
交于
、
两点,线段
的垂直平分线交
轴于点
,当点T到直线l距离为
时,求直线
方程和线段AB长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb153959d3a84cc1f4846f6ffd3b015a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.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/28113019952b6f450435b9928a894751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(Ⅱ)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd9f041754c54e2790f8fdf434ab148f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2018-02-06更新
|
300次组卷
|
2卷引用:山东省滨州市邹平一中2018-2019学年高一下学期3月月考数学试题
名校
解题方法
8 . 已知两点
、
,动点
在
轴上的射影是
,且
.
(1)求动点
的轨迹方程;
(2)设直线
、
的两个斜率存在,分别记为
、
,若
,求点
的坐标;
(3)若经过点
的直线
与动点
的轨迹有两个交点
、
,当
时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4e568d9cd57c442f011a787ab8aaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c2124260496e9307d6448c0c943f0.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/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25819cc137ad08070db4652db1d66725.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.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/90a802efc6b05133a91833e2f7074586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ecceb75be8d4fe129fa91f6e9a9809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f296a8c0d5cd16af5ba0e16ac69cc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次