名校
1 . 过椭圆
上的任意一点M(不与顶点重合)作椭圆的切线交x轴于点N,O为坐标原点,过N作直线
的垂线交直线
于点P,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb7101fa9146fdec51d44b8bf481dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af4c1699af5847959a3c3f11862647a3.png)
A.既没最大值也没最小值 | B.有最小值没有最大值 |
C.有最大值没有最小值 | D.为定值 |
您最近一年使用:0次
名校
解题方法
2 . 已知椭圆
的右焦点为
,且离心率为
.三角形
的三个顶点都在椭圆上,设它的三条边AB、BC、AC的中点分别为D、E、M、且三条边所在直线的斜率分别为
、
、
,且
、
、
均不为0,O为坐标原点.若直线OD、OE、OM的斜率之和为1,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1142f3e7a330a26e35cb94ad5392c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.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/dbf434334b09cc0fdd4e86e84e6ceb00.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/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dddcb841e17cc8df9c1aa78bc1b12c1.png)
A.-1 | B.![]() |
C.![]() | D.![]() |
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名校
解题方法
3 . 黄金分割比
被誉为“人间最巧的比例”.离心率
的椭圆被称为“优美椭圆”已知一“优美椭圆”
的左右顶点分别为A,B;椭圆上有一动点P(异于椭圆的左右顶点),设直线
,
斜率分别为
,则
为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb0c97c7ae2edee5470de05fa6d93f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a9076c3fe0b46b3206c21725c236f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e338d3759ec134b9b10b346e43e07fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c407500c3f3d395fdfdc366851ef3fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 设
为椭圆
上的动点,
为椭圆
的焦点,
为
的内心,则直线
和直线
的斜率之积( )
![](https://img.xkw.com/dksih/QBM/2022/1/5/2887837061980160/2953229596418048/STEM/5b21ca95-4eed-413b-b2ed-2ad7fe9a00e4.png?resizew=171)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e8add784e2db2e6a22254cf4d1b1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/025a8adfc778705f914bc4bf825774ac.png)
![](https://img.xkw.com/dksih/QBM/2022/1/5/2887837061980160/2953229596418048/STEM/5b21ca95-4eed-413b-b2ed-2ad7fe9a00e4.png?resizew=171)
A.是定值 | B.非定值,但存在最大值 |
C.非定值,但存在最小值 | D.非定值,且不存在最值 |
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2022-04-07更新
|
1165次组卷
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5卷引用:黑龙江省哈尔滨市第一中学校2022-2023学年高二上学期11月月考数学试题
黑龙江省哈尔滨市第一中学校2022-2023学年高二上学期11月月考数学试题(已下线)专题3.6 直线与椭圆的位置关系-重难点题型检测-2021-2022学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)第13讲 椭圆(4)浙江省宁波市北仑中学2021-2022学年高一(1班)下学期期中数学试题(已下线)重难专攻(九)?圆锥曲线中的定值问题(B素养提升卷)
5 . 已知椭圆
的左、右焦点分别是
,左、右顶点分别是
,点
是椭圆
上异于
的任意一点,则下列说法正确的个数是( )
(1)
;
(2)存在点
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f9bdc6d9f09e14b037ea7d3ee1f623.png)
(3)直线
与直线
的斜率之积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ac3f68b051e93e594669beca25ff91.png)
(4)若△
的面积为
,则点
的横坐标为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18eb0ffb0887c48286471688f158733b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ddaa027ce520c1c035399c3674bf39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5379ca02a94af1e74e5e00e38ba6e327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b81026b0db851a167ca4d2d06e3d71b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35bb8ca50f11fb7f9c2b96fd42b11a28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0b1a93ef14b1120f13b2749a5ba4f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b81026b0db851a167ca4d2d06e3d71b0.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f35dd7ceaf01a4d30a6593bc9f1ac7d.png)
(2)存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35bb8ca50f11fb7f9c2b96fd42b11a28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f9bdc6d9f09e14b037ea7d3ee1f623.png)
(3)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ef7d4c145c63af2069809796a0c95f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46b053f98b1d05a2043e94eeaefea87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ac3f68b051e93e594669beca25ff91.png)
(4)若△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8a7029669bf1774a24f3ef6273ca88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbff61fe9d4e93d7cc338489d1c99c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35bb8ca50f11fb7f9c2b96fd42b11a28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18eb0ffb0887c48286471688f158733b.png)
A.1 | B.2 | C.3 | D.4 |
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6 . 已知
、
是椭圆
长轴的两个端点,
、
是椭圆上关于
轴对称的两点,直线
、
的斜率分别为
、
.若椭圆的离心率为
,则
的最小值为( )
![](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/7dd54b9df3402ad91e2d34c40efe0c7a.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8c2d0ed3cffe8f28425cccc85e38bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9691613aae1a69934d3e3d2d599f748.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 已知
,
是椭圆
上关于原点对称的两点,
是该椭圆上不同于
,
的一点,若直线
的斜率
的取值范围为
,则直线
的斜率
的取值范围为( )
![](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/f64b7ab668d61bcb8ec6d195c672a81e.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa160f80772cd0b0b34dc7f4c1ba1249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-04-01更新
|
979次组卷
|
9卷引用:黑龙江省齐齐哈尔市实验中学2022-2023学年高二上学期第一次月考(9月)数学试题
黑龙江省齐齐哈尔市实验中学2022-2023学年高二上学期第一次月考(9月)数学试题陕西省2021届高三下学期教学质量检测测评(三)文科数学试题高考全国卷地区2021届3月联考乙卷数学(文科)试题(已下线)“超级全能生”2021届高三全国卷地区3月联考试题(甲卷)数学(文)试题安徽省宣城中学2020-2021学年高二下学期期中文科数学试题(已下线)3.1.2 椭圆的简单几何性质(精练)-2021-2022学年高二数学一隅三反系列(人教A版2019选择性必修第一册)(已下线)专题13 解析几何中的范围、最值和探索性问题(练)--第一篇 热点、难点突破篇-《2022年高考数学二轮复习讲练测(浙江专用)》(已下线)3.1椭圆B卷新疆乌鲁木齐市第五中学2024届高三上学期10月月考数学试题
8 . 设点
为椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
上的动点(除左右顶点外),椭圆
的焦点为
,离心率为
,
为
的内心,则直线
和直线
的斜率之积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9df1061c3ba5151ba2f7359acaf356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e8add784e2db2e6a22254cf4d1b1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/025a8adfc778705f914bc4bf825774ac.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2020-10-16更新
|
634次组卷
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4卷引用:黑龙江省大庆实验中学2020-2021学年高二10月月考数学(理)试题
9 . 已知
,
分别为椭圆
的左、右焦点,
是椭圆上的一点,且在
轴的左侧过点
作
的角平分线的垂线,垂足为
,若
(
为坐标原点)则
等于( )
![](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/8ddab7b8aa22e1ba4c59da7dc04ac9e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22a3c7e465a61e9849dd223261be47c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe955af255473d799edcade0dd186b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e85e60d90db39871b663b4ffdedd349.png)
A.4 | B.2 | C.![]() | D.![]() |
您最近一年使用:0次
2020-04-24更新
|
483次组卷
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5卷引用:黑龙江省齐齐哈尔市第八中学2020-2021学年高二上学期期中考试数学(理)试题
黑龙江省齐齐哈尔市第八中学2020-2021学年高二上学期期中考试数学(理)试题2020届全国100所名校最新高考模拟示范卷高三模拟测试理科数学(二)甘肃省兰大附中2020届高三5月月考数学(理科)试题(已下线)第九单元 解析几何(B卷 滚动提升检测)-2021年高考数学(理)一轮复习单元滚动双测卷(已下线)3.1.2 椭圆的简单几何性质(2)-2020-2021学年高二数学课时同步练(人教A版选择性必修第一册)
名校
解题方法
10 . 已知P是椭圆
上一点,点
分别是椭圆的左、右焦点,直线
交椭圆于另一点A,则
的周长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d856cc32b6bfe930328d9b6bf75fe5cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bce5a69e50ba0fc9e19ba0b15a10a42.png)
A.10 | B.16 | C.20 | D.40 |
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