1 . 已知椭圆
的右焦点
关于直线
对称的点在椭圆上,则椭圆的离心率为___ .
![](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/2d585d2d6643471640905d234d9538c5.png)
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2 . 以下四个命题中,正确的有__________ .
①函数的最值一定是极值;
②设
:实数
,
满足
;
:实数
,
满足
则
是
的充分不必要条件;
③已知椭圆
与双曲线
的焦点重合,
、
分别为
、
的离心率,则
,且
;
④菱形是圆的内接四边形或是圆的外切四边形.
①函数的最值一定是极值;
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5fcb02ff7ce397f5d33635b53f0c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f0756203fc98c430cdf6563666a079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
③已知椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4f38fb44a5f2b8889363eea2fd759a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ab85c65a034b483f6b44fac7a98cc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7091d529281abff275ef19b9197445a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff5d2c9fef4b8f717464077e8690275.png)
④菱形是圆的内接四边形或是圆的外切四边形.
您最近一年使用:0次
3 . 设椭圆
的右焦点为F,离心率为e,直线AB的斜率为k,A,B为椭圆上关于原点对称的两点,AF、BF的中点分别为M、N,以线段MN为直径的圆过原点
若
,则e的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00df4f17848c072b51e80d427d486e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e912a4a72a44aedaea6d7db5391869a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/000b31af420de87fbfe0d44e9e92b365.png)
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4 . 如图所示,点A,F分别是椭圆
的下顶点和右焦点交于另一点B,过中心O作直线AF的平行线交椭圆于点C,若
,则椭圆的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d125266f7bffeb5292742d81fd65432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/690e08e42165a9b9052a9a8d57345e87.png)
![](https://img.xkw.com/dksih/QBM/2018/12/7/2091540660969472/2093607535083520/STEM/8b10939df9e34449b2e1d7f0f88d5f14.png?resizew=198)
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名校
解题方法
5 . 已知点
是抛物线
:
与椭圆
:
的公共焦点,
是椭圆
的另一焦点,P是抛物线
上的动点,当
取得最小值时,点P恰好在椭圆
上,则椭圆
的离心率为_______ .
![](https://img.xkw.com/dksih/QBM/2019/1/8/2114189458849792/2115618741764096/STEM/f6adb7a4e04643269a001ead24598d82.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2019/1/8/2114189458849792/2115618741764096/STEM/fee25de7e6e84b7ab60a68e3858e585b.png?resizew=14)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48f28aeccf369df5980ac787e9e313f.png)
![](https://img.xkw.com/dksih/QBM/2019/1/8/2114189458849792/2115618741764096/STEM/915bc40e39ef43b6aa64037769e72acd.png?resizew=14)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af95e1aebe75c904be4e7f4ac12f7db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e84e3a6855369ad6cb75ad7874f5d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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2018-05-19更新
|
3057次组卷
|
6卷引用:浙江省温州市温州中学2023-2024学年高二上学期12月月考数学试题
浙江省温州市温州中学2023-2024学年高二上学期12月月考数学试题安徽省阜阳市阜阳一中2023-2024学年高二下学期开学检测数学试题【全国市级联考】山东省烟台市2018届高三高考适应性练习(二)数学(理)试卷【全国百强校】河北省武邑中学2019届高三12月月考数学(理)试题(已下线)专题9-1 圆锥小题压轴九类-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)山东省青岛市第五十八中学2024届高三上学期期末数学试题
名校
6 . 椭圆
,直线
,直线
,
为椭圆上任意一点,过
作
且与直线
交于点
,作
且与
交于点
,若
为定值,则椭圆的离心率为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0dce10bf671cc2ebc67aa7fd568a9a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/226c5951ef57a707f8ca3f26121b4ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de23fdaa48ca37352401166655668831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0d2e00213d588f2853271451045b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba266563f914e258c3c2a05aab6e47f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45fd889345e29d3930f24438ba95d409.png)
您最近一年使用:0次
2018-04-25更新
|
1565次组卷
|
4卷引用:【全国百强校】福建省厦门第一中学2017-2018学年高二下学期第二次月考数学(理)试题
【全国百强校】福建省厦门第一中学2017-2018学年高二下学期第二次月考数学(理)试题重庆市江北中学2020-2021学年高二上学期11月月考数学试题【全国市级联考】浙江省嘉兴市2018届高三4月模拟测试数学试题(已下线)《2018,我的高考我的教师君》-【考前预测篇1】热点试题精做
7 . 在直角坐标系内,点
实施变换
后,对应点为
,给出以下命题:
①圆
上任意一点实施变换
后,对应点的轨迹仍是圆
;
②若直线
上每一点实施变换
后,对应点的轨迹方程仍是
,则
;
③椭圆
上每一点实施变换
后,对应点的轨迹仍是离心率不变的椭圆;
④曲线
上每一点实施变换
后,对应点的轨迹是曲线
,
是曲线
上的任意一点,
是曲线
上的任意一点,则
的最小值为
.
以上正确命题的序号是___________________ (写出全部正确命题的序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f109ad046f362d8686c7ef9810c568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4c90c76ee3935ed1ecd104cf7614d9.png)
①圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba1080e317bb6747100220e00ede9dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba1080e317bb6747100220e00ede9dd.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02f266bd253738e315e84231235f0d2.png)
③椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
④曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c813b59e1ee4a7b2cf05c692c4aedd45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/250b5107cbd77faecb232faa478adfa4.png)
以上正确命题的序号是
您最近一年使用:0次
名校
8 . 设椭圆
的左右焦点分别为F1,F2,点P 在椭圆上运动,
的最大值为m,
的最小值为n,且m≥2n,则该椭圆的离心率的取值范围为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4972b23659a47c8bf56c0b78c9e1fec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd401c82c118e0fd5564af5f8dac3346.png)
您最近一年使用:0次
2018-04-22更新
|
1116次组卷
|
6卷引用:甘肃省张掖市2020-2021学年高二上学期期末数学(文)试题
甘肃省张掖市2020-2021学年高二上学期期末数学(文)试题(已下线)3.1 椭圆-2021-2022学年高二数学尖子生同步培优题典(人教A版2019选择性必修第一册)江西省崇仁一中、广昌一中、金溪一中2022-2023学年高二上学期第二次联考数学试题(已下线)北京市第四中学2023-2024学年高二下学期开学考试数学试题江西师范大学附属中学2018届高三4月月考数学(文)试题江西师范大学附属中学2018届高三4月月考数学(理)试题
9 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
的离心率为
,右焦点为
,点
在圆
上,且
在第一象限,过
作圆
的切线交椭圆于
,
两点.若
的周长为
,则椭圆
的方程为____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.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/50667ce76318b23b69ac6b8e16dc80d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2017-06-29更新
|
1520次组卷
|
2卷引用:湖北省武汉市重点中学4G+联合体2022-2023学年高二上学期期末联考数学试题
名校
10 . 已知椭圆C:
的左右焦点分别为
,
,点P在椭圆C上,线段
与圆:
相切于点Q,若Q是线段
的中点,e为C的离心率,则
的最小值是______________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.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/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8585676a37a64ce866ccf7723ccd0a8d.png)
您最近一年使用:0次
2017-04-12更新
|
3175次组卷
|
6卷引用:2016-2017学年河南省豫南六市高二下学期第一次联考数学(理)试卷