1 . 在平面直角坐标系
中,直线l 与抛物线W:
相切于点P ,且与椭圆
交于A,B两点.
(1)当P 的坐标为
时,求
;
(2)若点G 满足
求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97737a6ebb4f566c095f8c35a9af5042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1d0d75f5a2c5c8383c860fbf915fb11.png)
(1)当P 的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86022205a7487439dd8d0897cd3bf19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)若点G 满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5ff9650e5fac382f99f674af9a29299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3b785ebbf5889849e872f461669f71.png)
您最近一年使用:0次
名校
解题方法
2 . 在平面直角坐标系
中,设椭圆
的离心率为
,
,
分别是椭圆的左、右焦点,过
作两条互相垂直的直线
,
,直线
与
交于
,
两点,直线
与
交于
,
两点,且
的周长是
.
(1)求椭圆
的方程;
(2)当
时,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/014fb9d469a4b0b8a907ac416ad13585.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9c6fe12d3a9727e00ef87a630302ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09a8ac969e5cec3be6abf4ff44c692e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6758b8b074d33ea9e82818593656e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6758b8b074d33ea9e82818593656e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8f64ebec4a71a609204458cc54df82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea5c8fe935beac660eda538e59cd43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8f64ebec4a71a609204458cc54df82.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/eea5c8fe935beac660eda538e59cd43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e46c8b1425138338d06c88544229e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08ec3027d89a5c98f29b7a0e70c990d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b188a6a50dad3e47caa46f62ed52ddde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4457e3b494a948e0d98fe8bd0bab534.png)
您最近一年使用:0次
2024-04-22更新
|
844次组卷
|
4卷引用:山东省菏泽第一中学三校区联考2024届高三下学期5月月考数学试题
解题方法
3 . 在平面直角坐标系
中,椭圆
的离心率为
,直线
被
截得的线段长为
.
(1)求
的方程;
(2)已知直线
与圆
相切,且与
相交于
两点,
为
的右焦点,求
的周长
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b4bcb812c997db47214cb52c905f99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecfb02e157819a2bdd0f2790cbc825e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆
的右顶点为A,左焦点为F,椭圆W上的点到F的最大距离是短半轴长的
倍,且椭圆W过点
.记坐标原点为O,圆E过O、A两点且与直线
相交于两个不同的点P,Q(P,Q在第一象限,且P在Q的上方),
,直线
与椭圆W相交于另一个点B.
(1)求椭圆W的方程;
(2)求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/014b99f5c93a4ce8cd6251c12c1d1b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39cc033406da2cdd342308972c6701f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3306c91876abdcf71ac138b4077a9aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
(1)求椭圆W的方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcde52c2e252ca18148cbb9e48d213e4.png)
您最近一年使用:0次
2024-03-24更新
|
704次组卷
|
5卷引用:山东省菏泽第一中学八一路校区2024届高三下学期开学考试数学试题
5 . 已知椭圆
,直线
与
相交于
两点,
,若椭圆
恒过定点
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda696b103fe853f8fb814f601f080da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.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/6b74c320db15943bf1e34fc82c71d894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
A.![]() | B.![]() |
C.|AB|的长可能为3 | D.|AB|的长可能为4 |
您最近一年使用:0次
6 . 已知椭圆
的离心率
,其上焦点
与抛物线
的焦点重合.
(1)求椭圆
的方程;
(2)若过点
的直线交椭圆T于点
、
,同时交抛物线
于点
、
(如图1所示,点
在椭圆与抛物线第一象限交点上方),判断
与
的大小关系,并证明;
(3)若过点
的直线交椭圆
于点
、
,过点
与直线
垂直的直线
交抛物线
于点
、
(如图2所示),判断四边形
的面积是否存在最小值?若存在,求出最小值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa0cd3d7b5e005453c19e2172edc827c.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/61be090d2f56224b572047d9b36dc3d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/3ddec51d-ec77-4187-8df1-ec1b82d1b8b4.png?resizew=323)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若过点
![](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/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21448de9fe4710bf0d48138724832031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60436c1f7b5c2f6b5331548216e8077.png)
(3)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87391c2b154b302f4bf939035f59b99c.png)
您最近一年使用:0次
解题方法
7 . 已知椭圆
,其上焦点
与抛物线
的焦点重合.若过点
的直线
交椭圆
于点
,同时交抛物线
于点
(如图1所示,点
在椭圆与抛物线第一象限交点下方).
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/17/fa7a7929-983c-47c5-aed5-bd7c6d615562.png?resizew=266)
(1)求抛物线
的标准方程,并证明
;
(2)过点
与直线
垂直的直线
交抛物线
于点
(如图2所示),试求四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7eab4dd2a8332424ab484b069d4be7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.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/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/17/fa7a7929-983c-47c5-aed5-bd7c6d615562.png?resizew=266)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56163d3449960d6b9e29e72644a45de0.png)
(2)过点
![](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/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52041559f8fee18bfa3e2e2ac07c3bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87391c2b154b302f4bf939035f59b99c.png)
您最近一年使用:0次
8 . 已知在平面直角坐标系
中,椭圆
的左、右焦点分别为
,
,离心率
,
为椭圆
上任意一点,
面积的最大值为
.
(1)求椭圆
的方程;
(2)若斜率为
的直线
与圆
相切,且
与椭圆
相交于
,
两点,若弦长
的取值范围为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/075ba8c6fb5ef7288cd3fed425c8e69e.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/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b92075c4fff5c0a08fe4475fd29dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7db9b4ac9106bfaf32eba6ae265872b.png)
您最近一年使用:0次
2023-12-13更新
|
296次组卷
|
3卷引用:山东省菏泽市鄄城县第一中学2024届高三上学期1月月考数学试题
解题方法
9 . 已知椭圆
的左,右顶点分别为
,上,下顶点分别为
,四边形
的内切圆的面积为
,其离心率
;抛物线
的焦点与椭圆
的右焦点重合.斜率为k的直线l过抛物线
的焦点且与椭圆
交于A,B两点,与抛物线
交于C,D两点.
(1)求椭圆
及抛物线
的方程;
(2)是否存在常数
,使得
为一个与k无关的常数?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591b8af0ea4265a79680d742f2c0bfc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d468be20b4d43f5de75416de20e8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e5d91f4f631c580c155eba8c92bda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76dde16b05fba6fc61779511e63f34fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5bb267505c2a5fc6f9abc02bd43120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892e314e97750c0f54ecd98446d3c416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
(2)是否存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d80839153f2af7299b7593dd9fca104f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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6卷引用:山东省青岛莱西市2023届高三上学期质量检测(二)数学试题
山东省青岛莱西市2023届高三上学期质量检测(二)数学试题(已下线)专题突破卷23 圆锥曲线大题归类(已下线)重难点突破06 弦长问题及长度和、差、商、积问题(七大题型)-2(已下线)考点19 解析几何中的探索性问题 2024届高考数学考点总动员(已下线)专题07 双曲线与抛物线(讲义)(已下线)3.3.2 抛物线的简单的几何性质(AB分层训练)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)
名校
解题方法
10 . 已知过点的直线与椭圆
交于
、
两点,则弦长
可能是( )
A.1 | B.![]() | C.![]() | D.3 |
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8卷引用:山东省聊城市聊城一中东校等2校2023届高三上学期期末数学试题
山东省聊城市聊城一中东校等2校2023届高三上学期期末数学试题(已下线)考点巩固卷20 椭圆方程及其性质(十大考点)山东省济宁市泗水县2023-2024学年高二上学期期中数学试题2023届高三上学期一轮复习联考(五)数学试题(新高考卷)江西省宜春市万载县赣西外国语学校2023-2024学年高二上学期期中数学试题(A卷)江西省赣西外国语学校2023-2024学年高二上学期期中考试数学B卷(已下线)专题23 椭圆的简单几何性质10种常见考法归类(2)(已下线)专题10 椭圆的几何性质8种常见考法归类(2)