名校
解题方法
1 . 已知椭圆
:
的左顶点为
,焦距为
.动圆
的圆心坐标是
,过点
作圆
的两条切线分别交椭圆于
和
两点,记直线
、
的斜率分别为
和
.
(1)求证:
;
(2)若
为坐标原点,作
,垂足为
.是否存在定点
,使得
为定值?
![](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/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b728c0e69820cdcd839e67ffdb1014.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c922f835c095ce76ccef75e396b1cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
您最近一年使用:0次
2023-11-09更新
|
778次组卷
|
3卷引用:江西省宜春市铜鼓中学2023届高三上学期第三次阶段性测试数学试题
名校
2 . 用圆规画一个圆
,然后在圆内标记点
,并把圆周上的点
折叠到点
,连接
,标记出
与折痕
的交点
(如图),若不断在圆周上取新的点
,
,
.进行折叠并得到标记点
,
,
.设圆
的半径为4,点
到圆心
的距离为2,所有的点
,
,
,
形成的轨迹记为曲线
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/f5bd4676-7a48-4df9-a4d5-728eb50d2d4f.png?resizew=152)
(1)以
所在的直线为
轴,
的中垂线为
轴建立平面直角坐标系,求曲线
的标准方程;
(2)设直线
与曲线
交于
,
两点,且以
直径的圆经过曲线
的中心,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1652145a4785b50fa22fdd8c63f724b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1652145a4785b50fa22fdd8c63f724b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/f5bd4676-7a48-4df9-a4d5-728eb50d2d4f.png?resizew=152)
(1)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45018b0d8506401107f1eca44a55fa34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-11-15更新
|
257次组卷
|
2卷引用:江西省南昌市南昌县莲塘一中2022-2023学年高二上学期10月月考数学试题
名校
解题方法
3 . 已知椭圆C:
,点
,
分别为椭圆的左、右焦点.
(1)求椭圆C的短轴长和点
,
的坐标;
(2)设
为椭圆C上一点,且在第一象限内,直线
与y轴相交于点Q,若点
在以PQ为直径的圆的外部,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b99285432bd760aac3ae460752cdde0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
(1)求椭圆C的短轴长和点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83e02c09428538ce8ae136cff26d3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
4 . 已知椭圆
的离心率为
,
上的点P与
外的点
距离的最小值为2.
(1)求椭圆
的方程;
(2)若直线l与椭圆
交于点A,B,当直线l被圆
截得的弦长为2b时,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d2aff5570bd20fb94f9320551bd32c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e0b4cce429003557b051ea0fa2f7de.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(2)若直线l与椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b96eda0601673fafb836643969914f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
您最近一年使用:0次
2022-06-06更新
|
215次组卷
|
2卷引用:江西省南昌市2022届高三下学期核心模拟卷(中)数学(理)试题
名校
解题方法
5 . 已知椭圆
过点
,短轴一个端点到右焦点的距离为2.
(1)求椭圆
的方程;
(2)设过定点
的直线
与椭圆交于不同的两点A、B,若坐标原点
在以线段
为直径的圆外,求直线
的斜率
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef233ad3db01fa3ce9ee94eaad8e64e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25ce60648ea5042ab5eb5702efe651a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
6 . 设O为坐标原点,动点P在圆
上,过点P作
轴的垂线,垂足为Q且
.
(1)求动点D的轨迹E的方程;
(2)直线
与圆
相切,且直线
与曲线E相交于两个不同的点A、B,点T为线段AB的中点.线段OA、OB分别与圆O交于M、N两点,记
的面积分别为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b8628837ebfe0dae84f36cce491bac8.png)
(1)求动点D的轨迹E的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaecfbde526079d21c439cc4609be723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
名校
解题方法
7 . 已知椭圆
的右顶点为
,离心率为
.过点
与x轴不重合的直线l交椭圆E于不同的两点B,C,直线
,
分别交直线
于点M,N.
(1)求椭圆E的方程;
(2)设O为原点.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d295a4cc3a58f9f38ee98337313c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54695f96e6f365b0cc79b3ceaf5d26cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39cc033406da2cdd342308972c6701f1.png)
(1)求椭圆E的方程;
(2)设O为原点.求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5897b35e64d5c814ac47b917d45e88.png)
您最近一年使用:0次
2022-05-05更新
|
2650次组卷
|
8卷引用:江西省南昌市第十中学2022届高三下学期高考仿真模拟考试(一)数学(文)试题
名校
解题方法
8 . 已知椭圆
的短轴长为
,其离心率为
,已知双曲线
的渐近线方程为
,其离心率为
,且
.
(1)求椭圆C的标准方程;
(2)已知椭圆C的左焦点为F,过点F且不与坐标轴平行的直线l与椭圆相交于A,B两点,线段
的中垂线分别交x轴、y轴于M,N两点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fcb62a96dac6bd11b50a33fd8e64e3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6bb019e2d7c6d17d15ec4d9043f5e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7bcaf273474069ffe4d6e0db22e2cbf.png)
(1)求椭圆C的标准方程;
(2)已知椭圆C的左焦点为F,过点F且不与坐标轴平行的直线l与椭圆相交于A,B两点,线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b5a34215542bec52ba524bd6e304ac.png)
您最近一年使用:0次
名校
9 . 已知椭圆
的离心率为
,椭圆的中心
到直线
的距离为
.
(1)求椭圆
的方程;
(2)设过椭圆
的右焦点
且斜率为
的直线
和椭圆交于
两点,对于椭圆
上任意一点
,若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dccdc4f73b409dae07a0661a4281ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa82a15632a545ce2cc6dc998899807.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54bb99e14a2c48a600569891cb838069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1adebff9fb726cd58eda1ef994890901.png)
您最近一年使用:0次
2022-04-04更新
|
620次组卷
|
2卷引用:江西省八所重点中学2022届高三4月联考数学(文)试题
解题方法
10 . 已知椭圆
的离心率为
,P为椭圆E上一点,Q为圆
上一点,
的最大值为3(P,Q异于椭圆E的上下顶点).
![](https://img.xkw.com/dksih/QBM/2022/3/28/2946077197844480/2947290699497472/STEM/64b4427d51904c5592c7e6c5ed2b4bc1.png?resizew=231)
(1)求椭圆E的方程;
(2)A为椭圆E的下顶点,直线AP,AQ的斜率分别记为
,
,且
,求证:直线PQ过定点,并求出此定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
![](https://img.xkw.com/dksih/QBM/2022/3/28/2946077197844480/2947290699497472/STEM/64b4427d51904c5592c7e6c5ed2b4bc1.png?resizew=231)
(1)求椭圆E的方程;
(2)A为椭圆E的下顶点,直线AP,AQ的斜率分别记为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0aea8e4a6e524f43f9a13c1ef4fbddd.png)
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