1 . 历史上第一个研究圆锥曲线的是梅纳库莫斯(公元前375年—公元前325年),大约100年后,阿波罗尼斯更详尽、系统地研究了圆锥曲线,并且他还进一步研究了这些圆锥曲线的光学性质:如图,从椭圆的一个焦点出发的光线或声波,经椭圆反射后,反射光线经过椭圆的另一个焦点,其中法线
表示与椭圆
的切线垂直且过相应切点的直线,已知椭圆
的中心在坐标原点,焦点为
,
,若由
发出的光线经椭圆两次反射后回到
经过的路程为
.对于椭圆
上除顶点外的任意一点
,椭圆在点
处的切线为
,
在
上的射影为
,其中
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/13/73a2984c-7d8e-4af5-b174-b473b43382fc.png?resizew=173)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/12/94838805-95a5-400e-bbcf-08ab39ca7f84.png?resizew=197)
(1)求椭圆
的方程;
(2)如图,过
作斜率为
的直线
与椭圆
相交于
,
两点(点
在
轴上方).点
,
是椭圆上异于
,
的两点,
,
分别平分
和
,若
外接圆的面积为
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cddf5a506a90d09af01b81db43f17e93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799af451da9b732f1a9164ddcf49ae13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/0f85fca60a11e1af2bf50138d0e3fe62.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/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a6af050e5721febcc8103b9a0805399.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/13/73a2984c-7d8e-4af5-b174-b473b43382fc.png?resizew=173)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/12/94838805-95a5-400e-bbcf-08ab39ca7f84.png?resizew=197)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)如图,过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bdac20e214b2cb3bd07f8d4778dcca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.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/5963abe8f421bd99a2aaa94831a951e9.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/183b6a0cef4256c9696a5bca31053da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a12a030f853a383a50fd889486c9f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2f9c3b578fc0598d5ec6c79404c6cc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274e29821dd4630a7182573b7c654f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e19e695795d6c124955e2c6ec0b46056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc26cbada73d210ae6101654e894ebc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2 . 已知椭圆E:
的离心率为
,A,B是它的左、右顶点,过点
的动直线l(不与x轴重合)与E相交于M,N两点,
的最大面积为
.
(1)求椭圆E的方程;
(2)设
是直线AM与直线BN的交点.
(i)证明m为定值;
(ii)试堔究:点B是否一定在以MN为直径的圆内?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d776a89f4fd29dccffe1040069d59ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆E的方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82aaa597a5aa6176863eda3fdf83e181.png)
(i)证明m为定值;
(ii)试堔究:点B是否一定在以MN为直径的圆内?证明你的结论.
您最近一年使用:0次
2023-03-26更新
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798次组卷
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3卷引用:湖南师范大学附属中学2023届高三三模数学试题
3 . 定义:一般地,当
且
时,我们把方程
表示的椭圆
称为椭圆
的相似椭圆.
为
上的动点,延长
至点
,使得
的垂直平分线与
交于点
,记点
的轨迹为曲线
,求
的方程;
(2)在条件(1)下,已知椭圆
是椭圆
的相似椭圆,
是椭圆
的左、右顶点.点
是
上异于四个顶点的任意一点,当
(
为曲线
的离心率)时,设直线
与椭圆
交于点
,直线
与椭圆
交于点
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472393b18c7880e73b40e31fbe2d951c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee1845bf48cdfce200e466bd327c78e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a18d46cc66a208677f6a3f1e79e561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8d03478b85373a52ed3f3706ae7b76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3a9b723303acf1669d4d88a7172b99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8ad9e94d07405a6be585f81a0d623b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55620fce789bf9cd4a72ed5ba746c7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbdbe9a17a23c44cec8c7475c4dc1a9.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)在条件(1)下,已知椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a18d46cc66a208677f6a3f1e79e561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b6239db84396d617f152a65098c8faf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a18d46cc66a208677f6a3f1e79e561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a18d46cc66a208677f6a3f1e79e561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a9f26eea0ada26e96bce687c9447e4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5610f2c5b55ec06ba09cd553659794.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/5ddaa44e947bdcebc64a5f45809953de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45d4785a48c4e9641450e9ee2822df3.png)
您最近一年使用:0次
2023-03-03更新
|
902次组卷
|
3卷引用:湖南省长沙市雅礼中学2023届高三下学期月考(七)数学试题
名校
解题方法
4 . 如图,已知椭圆
与等轴双曲线
共顶点
,过椭圆
上一点P(2,-1)作两直线与椭圆
相交于相异的两点A,B,直线PA、PB的倾斜角互补,直线AB与x,y轴正半轴相交,分别记交点为M,N.
(2)若直线AB与双曲线
的左,右两支分别交于Q,R,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e6314e24c0225d455415c52124052b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e04c8d7fbd6165d240cad25eaef7b8ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若直线AB与双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fbac86947f24d80503333eed69e0427.png)
您最近一年使用:0次
2023-01-02更新
|
1333次组卷
|
2卷引用:湖南省长沙市雅礼中学2022-2023学年高三上学期月考(五)数学试题
5 . 已知椭圆C:
的右焦点为F,上顶点为
,下顶点为
,
为等腰直角三角形,且直线
与圆
相切.
(1)求椭圆C的方程;
(2)过
的直线l交椭圆C于D,E两点(异于点
,
),直线
,
相交于点Q.证明:点Q在一条平行于x轴的直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae54b78e906f865fbdb351ffb4d335f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fee2afdacb11a6d025578bcaf576d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
(1)求椭圆C的方程;
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c10f14aae6fb21e047ecb39cdf40c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f1158eaa2e338f564eb18de5bef1d25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e1bca493e452800f697c5c640b4aa3.png)
您最近一年使用:0次
2022-12-21更新
|
529次组卷
|
3卷引用:湖南省长沙市A佳教育联盟2022-2023学年高三上学期12月联考数学试题
湖南省长沙市A佳教育联盟2022-2023学年高三上学期12月联考数学试题湖南省株洲市部分学校2022-2023学年高三上学期12月联考数学试题(已下线)专题13 圆锥曲线压轴解答题常考套路归类(精讲精练)-1
名校
解题方法
6 . 已知椭圆
的长轴长为6,椭圆短轴的端点是
,
,且以
为直径的圆经过点
.
(1)求椭圆C的方程;
(2)设过点M且斜率不为0的直线交椭圆C于
两点.试问x轴上是否存在定点P,使PM平分
?若存在,求出点P的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79d247aef0e583d625d00a6e72db87a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0758f3ff9f1f7109024c1ef65536c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcfae259f4d3fe55be91c4480d24c5b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb735b9596d3bb79ad2cd9d8263c792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef50c3a02851941cda6752ed23834fb.png)
(1)求椭圆C的方程;
(2)设过点M且斜率不为0的直线交椭圆C于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85af7dc06bccad38c31fa6c8a564837b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c43824e0633b697ae98cce42d4737e0d.png)
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2022-10-21更新
|
858次组卷
|
6卷引用:湖南省长沙同升湖实验学校2022-2023学年高三上学期第三次月考数学试题
名校
解题方法
7 . 已知
的左,右焦点分别为
,
,长轴长为4,点
在椭圆C外,点Q在椭圆C上,则下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79d247aef0e583d625d00a6e72db87a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e82fe25db889399bb3ca4ffd5dd5db84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b2072de3e24c70c241d020a591378e.png)
A.椭圆C的离心率的取值范围是![]() |
B.已知![]() ![]() ![]() |
C.存在点Q使得![]() |
D.![]() |
您最近一年使用:0次
2022-10-17更新
|
1033次组卷
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6卷引用:湖南省长沙市宁乡市第一高级中学2022-2023学年高三上学期12月月考数学试题
8 . 设
为椭圆
:
的右焦点,过点
且与
轴不重合的直线
交椭圆
于
,
两点.
(1)当
时,求
;
(2)在
轴上是否存在异于
的定点
,使
为定值(其中
,
分别为直线
,
的斜率)?若存在,求出
的坐标;若不存在,请说明理由.
![](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/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a914673c349b73ce2c595b8971972b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db36eb152e1ee9a6c138b30ad2ced0aa.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a60ebd73abe0a3f8b0c9eff8164df76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9e81e69a74df3f61e90b3ce0e97e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6105ce854fe02662a1238be7bc30d55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2022-09-03更新
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764次组卷
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4卷引用:湖南省长沙市弘益高级中学2022-2023学年高三上学期第四次月考数学试题
名校
解题方法
9 . 设
分别是圆
的左、右焦点,M是C上一点,
与x轴垂直.直线
与C的另一个交点为N,且直线MN的斜率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
(1)求椭圆C的离心率.
(2)设
是椭圆C的上顶点,过D任作两条互相垂直的直线分别交椭圆C于A、B两点,过点D作线段AB的垂线,垂足为Q,判断在y轴上是否存在定点R,使得
的长度为定值?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183b6a0cef4256c9696a5bca31053da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b67528f875a6d4bac8bbf784f7b66a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
(1)求椭圆C的离心率.
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5fcce10d4243fb2a8351db179c2c48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c1abc6783970c158793a5e50d82e43f.png)
您最近一年使用:0次
2022-08-31更新
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1881次组卷
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8卷引用:湖南师范大学附属中学2023届高三上学期第一次月考数学试题
湖南师范大学附属中学2023届高三上学期第一次月考数学试题湖南省部分校2022-2023学年高三上学期入学检测数学试题(已下线)专题8 求定点定值运算(提升版)(已下线)专题31 圆锥曲线的垂直弦问题-1(已下线)重难点突破08 圆锥曲线的垂直弦问题 (八大题型)江苏省扬州市邗江中学2022-2023学年高二上学期期中数学试题(已下线)第三章 圆锥曲线(单元综合测试)-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选择性必修第一册)(已下线)第26讲 圆锥曲线中定值问题(1)
名校
解题方法
10 . 如图,已知椭圆
,其左、右焦点分别为
,过右焦点
且垂直于
轴的直线交椭圆于第一象限的点
,且
.
![](https://img.xkw.com/dksih/QBM/2022/5/30/2990814569807872/2991817147039744/STEM/e2e8ea58-58ac-4f6d-a9f4-a6b0bf5a52b0.png?resizew=245)
(1)求椭圆
的方程;
(2)过点
且斜率为
的动直线
交椭圆于
两点,在
轴上是否存在定点
,使以
为直径的圆恒过这个点?若存在,求出点
的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069ffc1e3936d254303d588e1a70a3aa.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4904e3977fcaf83a692e61b4d59b0fe7.png)
![](https://img.xkw.com/dksih/QBM/2022/5/30/2990814569807872/2991817147039744/STEM/e2e8ea58-58ac-4f6d-a9f4-a6b0bf5a52b0.png?resizew=245)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6831c6674f4bf86df7c8dd730e1c187d.png)
![](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/01c74a907dda6bb7d9d56d009d9df253.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2022-06-01更新
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3419次组卷
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8卷引用:湖南省长沙市雅礼中学2022届高三下学期二模数学试题
湖南省长沙市雅礼中学2022届高三下学期二模数学试题(已下线)专题24 圆锥曲线中的存在性、探索性问题 微点3 圆锥曲线中的存在性、探索性问题综合训练(已下线)专题38 圆锥曲线中的圆问题-2(已下线)重难专攻(十)圆锥曲线中的定点问题(核心考点集训)江西省南昌市2022-2023学年高二上学期末质量检测数学模拟试题山东省枣庄市滕州市2022-2023学年高二上学期期末数学试题(已下线)第25讲 圆锥曲线直线圆过定点问题-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选择性必修第一册)广东省东莞中学、惠州一中、深圳实验、珠海一中、中山纪念中学五校2022-2023学年高二下学期联考数学试题