解题方法
1 . 已知
为圆
上一动点,
在
轴,
轴上的射影分别为点
,
,动点
满足
,记动点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)过点
的直线与曲线
交于
,
两点,判断以
为直径的圆是否过定点?求出定点的坐标;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b24fa9f97addec1bae4ff823217db4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb10b0f4e81d280c9ccd1edba560cbcf.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/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2 . 设椭圆
的左、右焦点分别为
,
,上顶点为
,过点
与
垂直的直线交
轴负半轴于点
,且
.
(1)求椭圆
的方程;
(2)过椭圆
的右焦点
作斜率为1的直线
与椭圆
交于
两点,试在
轴上求一点
,使得以
,
为邻边的平行四边形是菱形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77d98da0e2532648a4435045ae73de2a.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78989dbf0fd940837d5c2cd19dbf052.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/7789a500686c7a73770404ead6af0590.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/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
您最近一年使用:0次
2019-06-11更新
|
443次组卷
|
3卷引用:【市级联考】山东省聊城市2019届高三三模文科数学试题
3 . 已知
是关于
的方程
的两个不等实根,则经过两点
的直线与椭圆
公共点的个数是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa392124b18f072afe74f7908df8d22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5b416b47c1b8c8c50abfd0fb8ac5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d12ebd10f6c0bcf98be52c32b107f1.png)
A.![]() | B.![]() | C.![]() | D.不确定 |
您最近一年使用:0次
4 . 在直角坐标系
中,设椭圆
的左焦点为
,短轴的两个端点分别为
,且
,点
在
上.
(Ⅰ)求椭圆
的方程;
(Ⅱ)若直线
与椭圆
和圆
分别相切于
,
两点,当
面积取得最大值时,求直线
的方程.
![](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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f36035f502830906ad9d235a7a66306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e38398209c6e596145044d5afdea2e80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/125d7a3870ca37c558239a45214d3568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/b45b8b000c9c286bff8a480dbf03b513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2019-05-19更新
|
628次组卷
|
2卷引用:山东省威海市2019届高三二模考试数学(理科)试题
名校
5 . 在平面直角坐标系中,若
,
,且
.
(Ⅰ)求动点
的轨迹
的方程;
(Ⅱ)设(Ⅰ)中曲线
的左、右顶点分别为
、
,过点
的直线
与曲线
交于两点
,
(不与
,
重合).若直线
与直线
相交于点
,试判断点
,
,
是否共线,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d908933bae3fc4d3525f1a6415abec25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dae0cdb2b8fa89d3bc8efa73501ff31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466b8d54c992f259df34b5d6de1c2760.png)
(Ⅰ)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ff7e0ef1f622120cc1b18e9d3e80ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)设(Ⅰ)中曲线
![](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/53a948d2f7732d7f03e986c63712089b.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2019-05-12更新
|
1521次组卷
|
4卷引用:【市级联考】山东省济宁市2019届5月高考模拟考试(二模)理科数学试题
6 . 如图,已知抛物线C:y2=2px(p>0),G为圆H:(x+2)2+y2=1上一动点,由G向C引切线,切点分别为E,F,当G点坐标为(-1,0)时,△GEF的面积为4.
(Ⅰ)求C的方程;
(Ⅱ)当点G在圆H:(x+2)2+y2=1上运动时,记k1,k2分别为切线GE,GF的斜率,求|
|的取值范围.
(Ⅰ)求C的方程;
(Ⅱ)当点G在圆H:(x+2)2+y2=1上运动时,记k1,k2分别为切线GE,GF的斜率,求|
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926c63f7c9191bc4c15ecc8804899601.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/bc134c04-3d92-4fc6-9547-e6dfa59997de.png?resizew=164)
您最近一年使用:0次
名校
7 . 已知椭圆
的离心率为
,椭圆
截直线
所得的线段的长度为
.
(Ⅰ)求椭圆
的方程;
(Ⅱ)设直线
与椭圆
交于
两点,点
是椭圆
上的点,
是坐标原点,若
,判定四边形
的面积是否为定值?若为定值,求出定值;如果不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)设直线
![](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/01c74a907dda6bb7d9d56d009d9df253.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5771779f32a0ced02cc1c5e52367baf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b76ac232477ac6d4b0a36eded969d68.png)
您最近一年使用:0次
2019-04-29更新
|
1210次组卷
|
8卷引用:2020届山东省高三高考模拟数学试题
2020届山东省高三高考模拟数学试题【市级联考】湖南省株洲市2019届高三第二次教学质量检测(二模)文科数学试题2020届山东省高三下学期2月模拟数学试题2020届山东省滕州市第一中学高三3月线上模拟考试数学试题(已下线)备战2020年高考数学之考场再现(山东专版)01(已下线)第8篇——平面解析几何-新高考山东专题汇编(已下线)专题9.7 圆锥曲线综合问题(精讲)-2021年新高考数学一轮复习学与练(已下线)专题9.7 圆锥曲线综合问题 2022年高考数学一轮复习讲练测(新教材新高考)(讲)
名校
解题方法
8 . 已知椭圆
的左、右焦点分别为
,且椭圆上存在一点
,满足
.
(1)求椭圆
的标准方程;
(2)过椭圆
右焦点
的直线
与椭圆
交于不同的两点
,求
的内切圆的半径的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5439f5ff9bd5deec0f0ef35c6f605b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0dac53904bc8bccf1a4ad14cb810ac3.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42dfeedb1b7bf383520fd0853ff14f32.png)
您最近一年使用:0次
2019-04-18更新
|
1009次组卷
|
7卷引用:【校级联考】山东省安丘市、诸城市、五莲县、兰山区2019届高三4月模拟训练数学(文)试题
名校
9 . 已知椭圆
的离心率为
,且椭圆C过点
.
(1)求椭圆C的标准方程;
(2)过椭圆C的右焦点的直线l与椭圆C交于A、B两点,且与圆:
交于E、F两点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/014fb9d469a4b0b8a907ac416ad13585.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4d9ff190d74979422dae71751c6fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce68ab8a64165a8897e088e825bb9191.png)
(1)求椭圆C的标准方程;
(2)过椭圆C的右焦点的直线l与椭圆C交于A、B两点,且与圆:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fce0745e9ae53f8e79f897253c9c7a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ef8af5c95d8bf511747bc219b0d36c.png)
您最近一年使用:0次
2019-03-19更新
|
1177次组卷
|
4卷引用:【市级联考】山东省济宁市2019届高三第一次模拟考试数学(文)试题
【市级联考】山东省济宁市2019届高三第一次模拟考试数学(文)试题2020届山东省济宁市第一中学高三下学期二轮质量检测数学试题(已下线)第8篇——平面解析几何-新高考山东专题汇编(已下线)专题08 解析几何中的最值范围问题(第五篇)-备战2020年高考数学大题精做之解答题题型全覆盖
名校
10 . 已知椭圆
的左,右焦点分别为
,离心率为
,
是
上的一个动点.当
是
的上顶点时,
的面积为
.
(1)求
的方程;
(2)设斜率存在的直线
与
的另一个交点为
.若存在点
,使得
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c043d5e847c15f00af2c4633949680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设斜率存在的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.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/439e95540157803d4ac3cf61a49f50a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b7f5506d346be580063f97411fbf9a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2019-03-18更新
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780次组卷
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4卷引用:【全国百强校】山东省淄博实验中学2019届高三第二学期第一次(4月)教学诊断考试数学(文)试题