名校
解题方法
1 . 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
|
867次组卷
|
3卷引用: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
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(已下线)微考点6-3 圆锥曲线中的定点定值问题(三大题型)
名校
解题方法
2 . 已知椭圆
的短轴顶点为
,短轴长是4,离心率是
,直线
与椭圆C交于
两点,其中
.
(1)求椭圆C的方程;
(2)若
(其中O为坐标原点),求k:
(3)证明:
是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f7ca8cb5a206da2d29551ee371ad00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1a82716c9e6ec9b9fea6960d4c0210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19cec8590140afdeeed3e4ffcd565c7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac67e9a909472ab852d38d2ec66a1e1.png)
(1)求椭圆C的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95f56469332ff64b183d5b45460c0b23.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/783685fdd5c4887058479093be49ddf2.png)
您最近一年使用:0次
2023-01-17更新
|
696次组卷
|
2卷引用:辽宁省沈阳市浑南区东北育才学校2022-2023学年高二上学期期末数学试题
3 . 已知椭圆
:
的一个焦点与曲线
的焦点重合,且离心率为
.
(1)求椭圆
的方程
(2)设直线
:
交椭圆
于M,N两点.
①若
且
的面积为
,求
的值.
②若
轴上的任意一点到直线
与直线
(
为椭圆的右焦点)的距离相等,求证:直线
恒过定点,并求出该定点坐标
![](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/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27bc3a7f511eb588c096c5672d5da49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff921b08b3f7d7b3c53c14c9ccd3b756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f02028a3847c4807c2d3cf0ea7efb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆E:
,P为椭圆E的右顶点,O为坐标原点,过点P的直线l1,l2与椭圆E的另外一个交点分别为A,B,线段PA的中点为M,线段PB的中点为N.
(1)若直线OM的斜率为
,求直线l1的方程;
(2)若OM⊥ON,证明:直线AB过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def6b1847098dd39d653c77786cb4eba.png)
(1)若直线OM的斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
(2)若OM⊥ON,证明:直线AB过定点.
您最近一年使用:0次
2021-08-24更新
|
579次组卷
|
3卷引用:辽宁省大连市第八中学2021-2022学年高二上学期期中考试数学试题
解题方法
5 . 已知椭圆
的标准方程是
,设
是椭圆
的左焦点,
为直线
上任意一点,过
作
的垂线交椭圆
于点
,
.
(1)证明:线段
平分线段
(其中
为坐标原点);
(2)当
最小时,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc2518c64be54c16908f868034d8fa7.png)
![](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/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba53065eb180a682305fddb95d14b62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963111aff6952322dfaca75ae069873c.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)
(1)证明:线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be99fa94a1f3e4964fcc13a14fab9ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfda4ddd7c4071ce8565fc222a934fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
2020-05-15更新
|
275次组卷
|
2卷引用:2020届辽宁省辽南协作校高三第一次模拟考试数学理科试题
名校
解题方法
6 . 已知椭圆
的离心率为
,且
过点
.
(1)求椭圆
的方程;
(2)若直线
与椭圆
交于
,
两点(点
,
均在第一象限),且直线
,
,
的斜率成等比数列,证明:直线
的斜率为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e684712aade8dcebb62716843791034.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2020-09-06更新
|
1368次组卷
|
10卷引用:辽宁省辽阳市2018学届高三第一次模拟考试数学(文)试题
辽宁省辽阳市2018学届高三第一次模拟考试数学(文)试题广东省2018届高三第一次模拟考试数学(文)试题【全国百强校】云南省玉溪市一中2017-2018学年高二下学期期末考试数学(理)试题青海省西宁市大通回族土族自治县2019-2020学年高二上学期期末考试数学(文)试题人教A版(2019) 选择性必修第一册 第三章 圆锥曲线的方程 单元测试(已下线)专题07+圆锥曲线大题专项练习-2020-2021学年【补习教材·寒假作业】高二数学(人教A版2019)(已下线)专题15+圆锥曲线大题专项练习-2020-2021学年【补习教材·寒假作业】高二数学(理)(人教A版)(已下线)专题15+圆锥曲线大题专项练习-2020-2021学年【补习教材·寒假作业】高二数学(文)(人教A版)(已下线)专题15 圆锥曲线大题专项练习(已下线)专题15 圆锥曲线大题专项练习
7 . 已知离心率为
的椭圆
经过抛物线
的焦点
,斜率为1的直线
经过
且与椭圆交于
两点.
(1)求
面积;
(2)动直线
与椭圆有且仅有一个交点,且与直线
分别交于
两点,
为椭圆的右焦点,证明
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f663b1f65678d7a4706da3d0727be4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029d213f131f206f5f3520860de56690.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9a6eeeebf3cff569578d7366b755aa.png)
(2)动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec9924d2204a81ee287433057733a7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/264fe111254a9236289bff05c4b7a01d.png)
您最近一年使用:0次
名校
8 . 已知椭圆
(a>b>0)经过点
,且离心率为
.
(Ⅰ)求椭圆C的方程;
(Ⅱ)已知A(0,b),B(a,0),点P是椭圆C上位于第三象限的动点,直线AP、BP分别将x轴、y轴于点M、N,求证:|AN|•|BM|为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3f51aa8ae11b5fb2bbd253c27d7d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86a665785c47f87bfd0a856470b7c243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9c6fe12d3a9727e00ef87a630302ab.png)
(Ⅰ)求椭圆C的方程;
(Ⅱ)已知A(0,b),B(a,0),点P是椭圆C上位于第三象限的动点,直线AP、BP分别将x轴、y轴于点M、N,求证:|AN|•|BM|为定值.
您最近一年使用:0次
2019-05-06更新
|
822次组卷
|
4卷引用:【全国百强校】辽宁省鞍山市第一中学2018-2019学年高二上学期期中考试数学(理)试题
【全国百强校】辽宁省鞍山市第一中学2018-2019学年高二上学期期中考试数学(理)试题【全国百强校】辽宁省鞍山市第一中学2018-2019学年高二上学期期中考试数学(文)试题安徽省合肥市第六中学2018-2019学年高二下学期期末数学(理)试题(已下线)第39讲 斜率和积问题与定点定值问题-2022年新高考数学二轮专题突破精练
名校
9 . 已知焦点在
轴上的椭圆
过点
,且离心率为
.
(Ⅰ)求椭圆
的标准方程;
(Ⅱ)若直线
(
,
)与椭圆C交于两点A、B,点D满足
,经过点D及点
的直线的斜率为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.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/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae492a515a518e5997c11e414ed80965.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/840811d30d8779355a22c9b3cd909e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d001a9ba1fcdafe7354f90ed8d70fb7.png)
您最近一年使用:0次
名校
10 . 已知椭圆
的右焦点为
,过
的直线
交椭圆于
两点(直线
与坐标轴不垂直),若
的中点为
,
为坐标原点,直线
交直线
于
.
(Ⅰ)求证:
;(Ⅱ)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36bfcf494549dc07de73b3978b8cb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848f0a6a566d677429c364c2da9f6404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075bc6df108c9c2b3b5ac46bca7c8d3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a07daa7893c0aa4313394369303561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb19311babacf4f5989dd67ea863ec3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9133cdd06a03e22b25b6ba346a1a80f8.png)
您最近一年使用:0次
2018-11-28更新
|
1082次组卷
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5卷引用:【全国百强校】辽宁省实验中学2018-2019学年高二上学期期中考试数学(文)试题
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