名校
解题方法
1 . 经过椭圆
的左焦点
作倾斜角为
的直线
,直线
与椭圆相交于
两点,求
中点坐标及
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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解题方法
2 . 写出适合下列条件的椭圆的标准方程,
(1)焦点在
轴上,焦距为2,椭圆上的点到两焦点的距离之和为4;
(2)两个焦点在坐标轴上,且经过
和
两点;
(3)经过点
,焦点坐标分别为
;
(4)焦点在
轴上,经过点
,焦距为
.
(1)焦点在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)两个焦点在坐标轴上,且经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05215da8cba26d3a6f9bed73bad0ba83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c0602cda79d2821c78e168b272f46c.png)
(3)经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2c62408d73dde3599f467b88f22d7b.png)
(4)焦点在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
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解题方法
3 . 已知圆心为C的圆经过点
和
,且圆心C在直线
上,
(1)求圆C的标准方程.
(2)过点
作圆的切线,求切线方程
(3)求x轴被圆所截得的弦长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf5a6145990adf5574f0e0f2fc828ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6419152065edb8cabf887b65adb4a73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b979396a703fb14715ba39232f5786a.png)
(1)求圆C的标准方程.
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b85acb5a868b0ff2a17b1ca926dd43.png)
(3)求x轴被圆所截得的弦长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
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2023-12-20更新
|
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2卷引用:天津市第一百中学、咸水沽第一中学2023-2024学年高二上学期期中联考数学试题
4 . 设椭圆
的左右顶点分别为
,左右焦点
.已知
,
.
(1)求椭圆方程及离心率.
(2)若斜率为1的直线
交椭圆于A,B两点,与以
为直径的圆交于C,D两点.若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44979a143cb1b38219395d4ed45ed064.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cbcd330947081ded45a4cdb5e96b39.png)
(1)求椭圆方程及离心率.
(2)若斜率为1的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d95485530815641d3e7b21b4e73f2b68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
5 . 已知椭圆
(
)的长轴长是短轴长的2倍.
(1)求椭圆的离心率
;
(2)直线
过点
且与椭圆有唯一公共点
,
为坐标原点,当
的面积最大时,求椭圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
(1)求椭圆的离心率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c41b2f7ca11db3aaea46c69286adbce.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/25dd698d57d1cf239eb8752aecaaa4f4.png)
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2023-12-20更新
|
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|
4卷引用:天津市第一百中学、咸水沽第一中学2023-2024学年高二上学期期中联考数学试题
名校
解题方法
6 . 已知
的三个顶点坐标分别是
.
(1)求边
所在的直线的一般式方程;
(2)求
边上的中线
所在直线的一般式方程;
(3)求边
上的高所在直线的一般式方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55472b3a76c5b43ee25826473a809d50.png)
(1)求边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
(3)求边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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解题方法
7 . 已知双曲线
(
,
)的左右焦点分别为
,
,过
的直线
与圆
:
相切,与双曲线在第四象限交于一点
,且有
轴,则离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697c20fca284394bf5d5b9e5f6d952e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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/85a3c31a3ee596913d198aae09cd0a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce9a7ab181883910f06f7fbecc6ea25d.png)
A.3 | B.![]() | C.![]() | D.2 |
您最近一年使用:0次
2023-12-19更新
|
375次组卷
|
2卷引用:天津市第一百中学、咸水沽第一中学2023-2024学年高二上学期期中联考数学试题
8 . 已知圆
,直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d307bc2a49638bfec71a0215d8c6c65c.png)
(1)证明:不论
取什么实数时,直线
与圆
恒交于两点;
(2)求直线
被圆
截得的线段的最短长度以及此时直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920bd07e70b67be4b02dc676e44cb29f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d307bc2a49638bfec71a0215d8c6c65c.png)
(1)证明:不论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求直线
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
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9 . 如图,已知椭圆
的左右顶点分别是
,
,焦点
,其中
,设点
,连接
交椭圆于点
,坐标原点是
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/6dfe213d-87f8-47a2-a26a-1a9da1464126.png?resizew=162)
(1)求椭圆的离心率;
(2)证明:
;
(3)设三角形
的面积为
,四边形
的面积为
,若
的最小值为1,求椭圆的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.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/24550b13dbecf7d86c7054250e987274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05d3b8f5c9df891ef6fbcaf12f43207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd81b31853a7d466db55dc2c6671f570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/6dfe213d-87f8-47a2-a26a-1a9da1464126.png?resizew=162)
(1)求椭圆的离心率;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ac6979adfa3b30c6067a9fdfd49f08.png)
(3)设三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f7c674f87a67fde99afceb3cfd8189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ad5a9147b25285124851a61c7d1a24a.png)
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10 . 已知点
,
,点C为圆
上一点,则
的面积的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29610a3415c1e795d35979a5a9ff69f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aacade1de64210bb11fa0dfe6c4343b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.12 | B.![]() | C.![]() | D.6 |
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2023-12-15更新
|
516次组卷
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3卷引用:天津市第一百中学、咸水沽第一中学2023-2024学年高二上学期期中联考数学试题
天津市第一百中学、咸水沽第一中学2023-2024学年高二上学期期中联考数学试题天津市东丽区2023-2024学年高二上学期期中数学试题(已下线)2.4.2 圆的一般方程【第二练】“上好三节课,做好三套题“高中数学素养晋级之路