名校
1 . 如图,椭圆
的左、右焦点分别为
,
,点
在椭圆上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/0a8cf05c-31a3-4e93-a8d7-81cdde3d7c58.png?resizew=215)
(1)求椭圆的方程;
(2)若A,B是椭圆上位于x轴上方的两点,直线
与直线
交于点P,
,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9d55173f26afdf0e37462b556a605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d6f746c2355072d914591bf60c3801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe8530b8e246a9a5ec9fe3b9c347d5a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/0a8cf05c-31a3-4e93-a8d7-81cdde3d7c58.png?resizew=215)
(1)求椭圆的方程;
(2)若A,B是椭圆上位于x轴上方的两点,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbad65b3d744b70da2480eee1cdb587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc1bb171ac77bb0246bb73114f83a4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
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2 . 已知椭圆
:
右焦点为
,右顶点为
,点
在椭圆上,且
轴,直线
交
轴于点
,若
;
(1)求椭圆的离心率;
(2)设经过点
且斜率为
的直线
与椭圆在
轴上方的交点为
,圆
同时与
轴和直线
相切,圆心
在直线
上,且
. 求椭圆的方程.
![](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/a0ed1ec316bc54c37c4286c208f55667.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/a6ce9cb2a356503a970d6466c75b564c.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455f8f7afe314139b898160e3f1391c1.png)
(1)求椭圆的离心率;
(2)设经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157b4ea52f231765d4de21d3515a5be5.png)
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2019-11-14更新
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558次组卷
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3卷引用:天津市六校(静海一中,杨村中学,宝坻一中,大港一中等)2019-2020学年高二上学期期中联考数学试题
名校
3 . 已知椭圆
的两焦点分别为
,长轴长为6.
⑴求椭圆
的标准方程;
⑵若直线
与椭圆
交于
、
两点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57cd95a369b942a3d2af35f6c97437c6.png)
⑴求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
⑵若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.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/294f5ba74cdf695fc9a8a8e52f421328.png)
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4 . 已知中心在坐标原点O的椭圆C经过点A(
),且点F(
,0)为其右焦点.
(1)求椭圆C的方程;
(2)是否存在直线与椭圆C交于B,D两点,满足
,且原点到直线l的距离为
?若存在,求出直线的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e524b650440dfc3ec94457555cc73537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆C的方程;
(2)是否存在直线与椭圆C交于B,D两点,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf4e7b42e4c4a3f5118e744072b3638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
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2019-11-12更新
|
739次组卷
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3卷引用:江西省南昌市东湖区第十中学2019-2020学年高二上学期期中数学试题
5 . 已知椭圆
的长轴长是短轴长的两倍,焦距为
.
(1)求椭圆
的标准方程;
(2)若直线
且
与椭圆
交于两点
,且
,试求直线
的斜率,并求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.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/0d3acbee2379c01491432a6ca38f8867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e464a3586f84fcdf7d221619f8018144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923da7cdcd2f64423415e1dedbffbf4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c3b112ec47db88d318e5068e9af947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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6 . 已知椭圆E的方程为
右焦点为
,直线
的倾斜角为
直线
与圆
相切于点Q,且点Q在
轴右侧,设直线
交椭圆E于两个不同点A、B.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/41cf9755-2f1a-48ae-aaf3-d5d68fd49c67.png?resizew=191)
(1)求直线
的方程;
(2)求△ABF的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412e1cd1477909974e6db5a8841e6758.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/8727480c1bee756b95cece8f18527cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49137970108f50350a3211aa0281faaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/41cf9755-2f1a-48ae-aaf3-d5d68fd49c67.png?resizew=191)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)求△ABF的面积.
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2019-11-09更新
|
1536次组卷
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3卷引用:上海市向明中学2018-2019学年高二下学期期中数学试题
上海市向明中学2018-2019学年高二下学期期中数学试题湖北省武汉市新洲区第三中学2020-2021学年高二上学期10月月考数学试题(已下线)重难点01:直线与椭圆的位置关系(分层练习)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第一册)
名校
7 . 已知抛物线
(
).
(1)若
上一点
到其焦点的距离为3,求
的方程;
(2)若
,斜率为2的直线
交
于A、B两点,交x轴的正半轴于点M,O为坐标原点,
,求点M的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49cd0e83c4f9a3239084f138107ea1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fbdf49cd00af1ff87259836ddd9f6b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5199549b47e180b07cb219ae40c9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.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/19468abe1aa4e99874d13b8359ec7332.png)
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2019-11-09更新
|
496次组卷
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5卷引用:上海市松江一中2022-2023学年高二下学期期中数学试题
上海市松江一中2022-2023学年高二下学期期中数学试题上海市闵行区2019届高三第一学期(一模)期末质量监控数学试题(已下线)2019年上海市闵行区高三上学期期末质量调研数学试题上海市东昌中学2019-2020学年高二上学期期末数学试题上海市吴淞中学2022-2023学年高二上学期期末数学试题
8 . 教材曾有介绍:圆
上的点
处的切线方程为
我们将其结论推广:椭圆
的点
处的切线方程为
在解本题时可以直接应用,已知直线
与椭圆E:
有且只有一个公共点.
(1)求
的值;
(2)设O为坐标原点,过椭圆E上的两点A、B分别作该椭圆的两条切线
,且
与
交于点M![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf278d3ece654fea3fdf89e532c685a9.png)
①设
,直线AB、OM的斜率分别为
,求证:
为定值;
②设
,求△OAB面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3503d330608e7138d1b529aba4512fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27477c4eba717135b559c18fb786e36b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f965cfee1311f0df39396b035770e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d891034f9d4ee622e083d44989b7fdc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27477c4eba717135b559c18fb786e36b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65adcbe574b14ad635df2c6f03f4822f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c93215f460bffca5bdae786eb42144b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98f8484a21113a5e5b933ab1b0c9114.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设O为坐标原点,过椭圆E上的两点A、B分别作该椭圆的两条切线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf278d3ece654fea3fdf89e532c685a9.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42623f14667ebfa914eb12d026023d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
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9 . 已知椭圆C:
(a>b>0)的离心率为
,且经过点P(2,2).
(1)求椭圆C的方程;
(2)过点Q(1,-1)的直线与椭圆C相交于M,N两点(与点P不重合),试判断点P与以MN为直径的圆的位置关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79280809958af38e84c2600749a63624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
(1)求椭圆C的方程;
(2)过点Q(1,-1)的直线与椭圆C相交于M,N两点(与点P不重合),试判断点P与以MN为直径的圆的位置关系,并说明理由.
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10 . 设
为坐标原点,动点
在圆:
上,过
作
轴的垂线,垂足为
,点
满
.
(1)求点
所在曲线
的方程;
(2)设直线
与曲线
相交于不同的两点
,当点
为曲线
的上顶点时,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22c87c39b56d58d1993c6725d9b75275.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/690327ef6afcce4e693cee02642835e6.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a33e5d0dbdd0f15854f0d7dd8b53058.png)
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