名校
1 . 已知椭圆
的右焦点是
,过点
作直线
交椭圆于点A,B,过点
与直线
垂直的射线交椭圆于点
,
,且三点
共线(其中O是坐标原点),则椭圆的离心率为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3324199c6751f2e0e6d8542783b0d957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/a0ed1ec316bc54c37c4286c208f55667.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/78b78af48c04c69f03e32b7ef055dc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b908ff79a3d103a3668b687b0e29fb.png)
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2024-05-08更新
|
1203次组卷
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2卷引用:辽宁省2024届高三下学期二轮复习联考(二)数学试题
解题方法
2 . 设双曲线
的左、右焦点分别为
,过
的直线与双曲线
的右支交于
两点,且
,则双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/ceb7f22768b5096b092c8de41c12917f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . (1)利用双曲线定义证明:方程
表示的曲线是焦点在直线
上的双曲线,记为曲线
;
(2)设点
在曲线
上,
在曲线
上,且满足
,求
方程;
(3)点
在
上,过点
的直线
与
的渐近线交于
,
两点,且满足
,求
(
为坐标原点)的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377a2333ff8c63cbdb20b882d6d5a7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb57bb18755127be041d346444a4743e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeebe2d626de76ae34a1a42b62a1a3bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eae0d794fb0823bc1545822f2f7b8db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/548e9d7ca152d84587b14b99749a339d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f02028a3847c4807c2d3cf0ea7efb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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名校
4 . 已知方程
表示的曲线是椭圆,则实数k的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/206417546e9edd2ea35f4a213c3fef32.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-05-02更新
|
1528次组卷
|
2卷引用:辽宁省部分学校2024届高三第二次联考(二模)数学试题
名校
解题方法
5 . 已知
是椭圆
上的动点,若动点
到定点
的距离
的最小值为1,则椭圆
的离心率的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446239fc6902eb55ad0e01d924faf592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56ab70e602f2e2e291df643ab209162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
6 . 抛物线
的焦点坐标是
,则焦点到准线的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071d4c1556de22088445f191a80b8a25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749b71e49c95b9212a600e837261ccdd.png)
A.1 | B.![]() | C.![]() | D.2 |
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2024-04-26更新
|
1228次组卷
|
4卷引用:辽宁省2024届高三下学期二轮复习联考(二)数学试题
7 . 已知椭圆
与抛物线
在第一象限的公共点为A,椭圆的左、右焦点分别为
,其中右焦点与抛物线的焦点重合,已知
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc7f90763882906f3a5a22aecbc6a6b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c6f26cc0ac7f7dd2bfe97312e39155.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 如图,已知过抛物线
(
)的焦点
的直线与抛物线交于
两点,过点A作抛物线的准线的垂线
,垂足为
,抛物线的准线与
轴交于点
,
为坐标原点,记
,
,
分别为
,
,
的面积.若
,则直线
的斜率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a07ff78c166793f5e8d23f0b7f4be8f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066afbd3603bccf7d9591c4ac48f552e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187e4941e2d8f5f8a1bb60f852588de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2024-04-22更新
|
852次组卷
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4卷引用:辽宁省鞍山市第一中学2024届高三下学期八模数学试卷
辽宁省鞍山市第一中学2024届高三下学期八模数学试卷湖北省黄石市第二中学2023-2024学年高三下学期三模考试数学试题河南省信阳市新县高级中学2024届高三4月适应性考试数学试题(已下线)四川省成都市外国语学校2024届高三高考模拟(五)理科数学试题
9 . 已知椭圆
的左右焦点分别为
,椭圆
的短轴长为
,离心率为
. 点
为椭圆
上的一个动点,直线
与椭圆
的另一个交点为
,直线
与椭圆
的另一个交点为
,设
,
.
(1)求椭圆
的方程;
(2)证明:
为定值;
(3)已知
,用
表示
的面积
,并求出
的最大值.
![](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/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.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/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678764669f89f7f7c1e2f986b642b466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5749effb19c4a35500b1b1162e33c24.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32705e629d8b9187b53efeee6605af15.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b170470d02c85c1be9a3faff5eca0de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8750c7a9d012d136a878dc8f4233dfb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc2dced088b495e46e255a8d8cd6f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc2dced088b495e46e255a8d8cd6f91.png)
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2024-04-22更新
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3卷引用:2024届辽宁省部分重点中学协作体高三下学期4月三模数学试卷
10 . 已知点P为双曲线
上任意一点,过点
的切线交双曲线
的渐近线于
两点.
(1)证明:
恰为
的中点;
(2)过点
分别作渐近线的平行线,与OA、OB分别交于M、N两点,判断
PMON的面积是否为定值,如果是,求出该定值;如果不是,请说明理由;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c2bef5c293a098d46919de91c03aab.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/01c74a907dda6bb7d9d56d009d9df253.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a5328919a7cec382c2e91c9c528fc1.png)
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