1 . 已知椭圆
:
,直线
:
交椭圆于M,N两点,T为椭圆的右顶点,
的内切圆为圆Q.
(1)求椭圆
的焦点坐标;
(2)求圆Q的方程;
(3)设点
,过P作圆Q的两条切线分别交椭圆C于点A,B,求
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b801e3da6f1b42d1f68cbf88cbfb4e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bf66a5f30d94390f59c6a3d1ae6c46.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求圆Q的方程;
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38cc4e8043fb27abccf766c5f314dfe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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2024高三·全国·专题练习
2 . 已知圆,椭圆
.
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)现有如下真命题:
①过圆上任意一点
作椭圆
的两条切线,则这两条切线互相垂直;
②过圆上任意一点
作椭圆
的两条切线,则这两条切线互相垂直.据此写出一般结论,并加以证明.
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2024高三·全国·专题练习
解题方法
3 . 如图所示,在棱长为4的正方体中,
为
的中点,
,
分别在
上移动,且
平分正方形
的面积.又
在平面
上的射影与
的交点为
,问在平面
内是否存在两个定点,使
到这两个定点的距离之和为定值?若存在,求出这两个定点;若不存在,请说明理由.
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解题方法
4 . 已知椭圆的焦点是椭圆
的顶点,椭圆
的焦点也是
的顶点.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654317ca05d25fee978869723ba8d0c8.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/937c5db73d81da5525d4d35885dac04f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
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2024高二·全国·专题练习
解题方法
5 . 根据条件分别求双曲线的标准方程:
(1)与双曲线
有共同渐近线,且过点
;
(2)与椭圆
有相同的焦点,其中一条渐近线为直线
.
(1)与双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c58fa4a337f0b81b991fb32e8e6e3c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c51a57e05032acb94d05a0cbcaaa5fc.png)
(2)与椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c763113a1fc48e8acc83787b8cd24eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc81cfaccc00aa4b7139de5a35a102.png)
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2024高三·全国·专题练习
解题方法
6 . 已知抛物线
的焦点和椭圆
的右焦点相同,点
的坐标分别为
是抛物线上的点,设直线
与抛物线的另一交点分别为
.
(1)求抛物线的标准方程;
(2)求证:当点
在抛物线上变动时(只要点
存在,且点
与点
不重合),直线
恒过定点,并求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c64cae1ba15d5030ef62460bbc708af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55fb7ec4aa413693f4ecae59fe0e2084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666e81326945f168fc30291f1bb2fc10.png)
(1)求抛物线的标准方程;
(2)求证:当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666e81326945f168fc30291f1bb2fc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f541f7ae7c39082d202efd28805c54e.png)
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2024-01-30更新
|
635次组卷
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3卷引用:新高考学科基地秘卷(十)
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7 . 已知双曲线过点
且与椭圆
有相同的焦点
,
(1)求双曲线的标准方程;
(2)若点
在双曲线上,且
,求
与
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d95ab554e5ba1078cd4d40425171d82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dce7445cd0f42c7f88dc3efcb72c7969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48932773034bb6e1651acf140d47822c.png)
(1)求双曲线的标准方程;
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4aaec620c8025f9bfe921aae8a04bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9795e5db34dcdc4d5af1eea3d433396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
8 . 已知
分别是椭圆
的左、右顶点,过点
、斜率为
的直线
交椭圆
于
两个不同的点.
(1)求椭圆
的焦距和离心率;
(2)若点
落在以线段
为直径的圆的外部,求
的取值范围;
(3)若
,设直线
分别交
轴于点
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b6b9e2970a57ad12a76d9a4c0b04c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bab45799f9f8d0374f529e8b30a0b27.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/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b14fa212bbddd28310d463fcdef7e62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8de18f5d726dbe53dee012b5013c834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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解题方法
9 . 设椭圆
:
的左、右顶点分别为C,D,且焦距为2.F为椭圆的右焦点,点M在椭圆上且异于C,D两点.若直线
与
的斜率之积为
.
(1)求椭圆
的标准方程;
(2)过点
作一条斜率不为0的直线与椭圆E相交于A,B两点(A在B,P之间),直线
与椭圆E的另一个交点为H,求证:点A,H关于x轴对称.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2e2c0d4ac2bd79f6cea7a9b1a50662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af74113f38fffeed8075e57d7f9d2533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
您最近一年使用:0次
2023-11-23更新
|
868次组卷
|
3卷引用:微考点6-3 圆锥曲线中的定点定值问题(三大题型)
(已下线)微考点6-3 圆锥曲线中的定点定值问题(三大题型)河南省开封市五县2023-2024学年高二上学期期中联考数学试题辽宁省沈阳市辽宁省实验中学2023-2024学年高二上学期12月月考数学试题
名校
解题方法
10 . 已知椭圆
:
的焦距为
,且
.
(1)求
的方程;
(2)A是
的下顶点,过点
的直线
与
相交于
,
两点,直线
的斜率小于0,
的重心为
,
为坐标原点,求直线
斜率的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9fa3babeb095d6078e2ee7eb9cdff2e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)A是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af74113f38fffeed8075e57d7f9d2533.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307bd991211ec79b47a4be52933bb8e7.png)
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2023-11-23更新
|
776次组卷
|
8卷引用:重难点7-2 圆锥曲线综合应用(7题型+满分技巧+限时检测)
(已下线)重难点7-2 圆锥曲线综合应用(7题型+满分技巧+限时检测)(已下线)模块一 专题2 解析几何(2)(已下线)模块三 专题5 大题分类练(解析几何)拔高能力练(已下线)专题03 圆锥曲线方程(2)四川省雅安市雅安市联考2023-2024学年高三上学期期中考试数学(理)试题四川省绵阳市绵阳实验高级中学2024届高三上学期11月月考数学(理)试题广西普通高中2024届高三跨市联合适应性训练检测卷数学试题广西桂林、柳州、贺州、崇左四市2024届高三上学期跨市联合适应性检测数学试题