名校
解题方法
1 . 设椭圆
:
(
)经过点
,且离心率
,直线
:
垂直
轴交
轴于
,过
的直线
交椭圆
于
,
两点,连接
,
,
.
的方程:
(2)设直线
,
的斜率分别为
,
.
(ⅰ)求
的值;
(ⅱ)如图:过
作
轴的垂线
,过
作
的平行线分别交
,
于
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afbbc53b8235d6c4831c82f155a8f933.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c663466d641b5fdfef1e529d6c330ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166afeb61d5a80366a8ae29c912cd644.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/d583183429b6b31aa9742eefc67d3181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设直线
![](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/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
(ⅱ)如图:过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d583183429b6b31aa9742eefc67d3181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/ea34d9a43af8cea2eeaa30229dc0ffd3.png)
您最近一年使用:0次
2024-06-08更新
|
310次组卷
|
2卷引用:黑龙江省大庆市实验中学实验二部2023-2024学年高三下学期阶段考试(二)数学试题
名校
2 . 加斯帕尔•蒙日(如图1)是18~19世纪法国著名的几何学家,他在研究圆锥曲线时发现:椭圆的任意两条互相垂直的切线的交点都在同一个圆上,其圆心是椭圆的中心,这个圆则被称为“蒙日圆”(如图2).已知矩形
的四边均与椭圆
相切,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ddaa027ce520c1c035399c3674bf39.png)
A.椭圆![]() ![]() |
B.椭圆![]() ![]() |
C.椭圆![]() ![]() |
D.矩形![]() |
您最近一年使用:0次
3 . 已知椭圆
的离心率为
,椭圆的右焦点
与抛物线
的焦点重合.
(1)求椭圆
的方程;
(2)设直线
与椭圆
交于
两点,与抛物线
交于
两点,若
为定值,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4fb72e39d79b7a0cd892fa5fa34bb7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9733c7408e2c9ace28486fa2fbb640b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40297ee651c3f2959a56a6cb751c68fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8630ade724bce35fefd437957a88476.png)
您最近一年使用:0次
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4 . 已知曲线
,其中
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a6567908622a20195c8423d1a3682b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211bb9d7aadd19ea6593f3bddcc6205b.png)
A.存在![]() |
B.存在![]() |
C.若C为椭圆,则![]() |
D.若C为双曲线,则![]() |
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5 . 已知椭圆方程为
,则下列说法错误 的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1538e111b91b0052feef223f1c0a4742.png)
A.![]() | B.存在m值使椭圆的离心率![]() |
C.椭圆的焦距不确定 | D.椭圆的焦点在y轴 |
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6 . 在平面直角坐标系xOy中,长、短轴所在直线不与坐标轴重合的椭圆称为“斜椭圆”,将焦点在坐标轴上的椭圆绕着对称中心顺时针旋转
,即得“斜椭圆”
,设
在
上,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c20e88a33043f4279fff360c81006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a315082c24416a968957e7f4905526c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.“斜椭圆”的焦点所在直线的方程为![]() | B.![]() ![]() |
C.旋转前的椭圆标准方程为![]() | D.![]() |
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解题方法
7 . 已知
分别是椭圆
的左、右焦点,过点
的直线交
于
两点,若
的最大值为8,则
的离心率为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a649464be49dd576a183bf4d04d441ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0df298d90f24e978db2af8ed07369dda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-05-01更新
|
295次组卷
|
3卷引用:黑龙江省牡丹江市第二高级中学2024届高三下学期高考考前热身卷(三)数学试题
解题方法
8 . 如图,已知椭圆
的左、右焦点分别为
,点M,N在
上,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50ba772d5b33715aefa57d448951b9ec.png)
,则
的离心率为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.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/50ba772d5b33715aefa57d448951b9ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda28e418f5c1d8e13919a394036f3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
解题方法
9 . 已知椭圆
的左顶点为
,过
且斜率为
的直线交
轴于点
,交
的另一点为
.
(1)若
,求
的离心率;
(2)点
在
上,若
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bdac20e214b2cb3bd07f8d4778dcca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2e2c225dc97361c2859fc7233620b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e595ee07ead402d0af6c4cee6531f6bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83c836dccadff9f4ea5d6fe3d76a438.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
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10 . 已知椭圆
的左、右焦点分别为
,上顶点为
,若过
且倾斜角为
的直线
交椭圆
于
两点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
A.![]() ![]() | B.![]() |
C.点![]() ![]() ![]() | D.![]() |
您最近一年使用:0次
2024-03-21更新
|
1274次组卷
|
4卷引用:黑龙江省双鸭山市第三十一中学等校2024届高三第二次模拟数学试题