设A是圆
上的任意一点,
是过点A与
轴垂直的直线,D是直线
与
轴的交点,点M在直线
上,且满足
.当点A在圆上运动时,记点M的轨迹为曲线
.
(1)求曲线
的标准方程;
(2)设曲线
的左右焦点分别为
、
,经过
的直线
与曲线
交于P、Q两点,若
,求直线
的方程.
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/df91cfb00655492db243948145693c99.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/4c5625acf5824aab8527f2acc0bf255d.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/ef55461254f94fdb9c9b9592eac70b92.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/6d7d71de58004fda981d32a5280504b5.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/ef55461254f94fdb9c9b9592eac70b92.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/6d7d71de58004fda981d32a5280504b5.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/e2ab05b91f2b4bac94e7a0a13fba1947.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/242c7bc53cd4491e8b6c4d467bbbbbbc.png)
(1)求曲线
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/242c7bc53cd4491e8b6c4d467bbbbbbc.png)
(2)设曲线
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/242c7bc53cd4491e8b6c4d467bbbbbbc.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/816177211014411bb838ec89f0521632.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/92780370ef3446c2a451bab8907eedd3.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/92780370ef3446c2a451bab8907eedd3.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/e0b475ce6cf547e4b46367c45d5694bc.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/242c7bc53cd4491e8b6c4d467bbbbbbc.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/820e246825a64befa874989b02a5b7c2.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/e0b475ce6cf547e4b46367c45d5694bc.png)
更新时间:2016-12-03 12:52:35
|
相似题推荐
解答题-问答题
|
较难
(0.4)
【推荐1】在平面直角坐标系
中,动点
到点
的距离与它到直线
的距离之比为
.
(1)求动点
的轨迹
的方程;
(2)设直线
与曲线
交于
两点,与
轴、
轴分别交于
两点(且![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/8b3526dbd3dd4fc1905a0b6b17ff8e18.png)
在
之间或同时在
之外). 问:是否存在定值
,对于满足条件的任意实数
,都有
的面积与
的面积相等,若存在,求
的值;若不存在,说明理由.
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/beda4f7f366f4c03a2543407d371acd5.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/f68b910387994bc4a4a1bc4aa3191b74.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/84b98a8cecdf4b8eb106a0983690e1f7.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/437565ea45a14b3ead4255336581b233.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/996ebd6fb5ff42f98e7c589eb410d9ad.png)
(1)求动点
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/f68b910387994bc4a4a1bc4aa3191b74.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/4e69986b4f5e419a926eeb9fd520a423.png)
(2)设直线
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/ab603cc3319944aba8935e34f9f88aee.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/4e69986b4f5e419a926eeb9fd520a423.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/b51a993afe1642dea10e6b8f32d1154c.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/11372e8433304bf584ebdf86cef82f2b.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/d942f810ae0e471395332ea03ff6ed34.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/8b3526dbd3dd4fc1905a0b6b17ff8e18.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/8b3526dbd3dd4fc1905a0b6b17ff8e18.png)
在
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/b51a993afe1642dea10e6b8f32d1154c.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/b51a993afe1642dea10e6b8f32d1154c.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/b928ec0a480b4a9baace0e814bcb782f.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/ae06034832fd4082b6da4efe97bb5fad.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/0bf85ad57bc940698ce5fb8f2552c855.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/2c580b79a1494b338fa7933effdfef69.png)
![](https://img.xkw.com/dksih/QBM/2016/8/18/1572984690147328/1572984696463360/STEM/b928ec0a480b4a9baace0e814bcb782f.png)
您最近一年使用:0次
【推荐2】已知
为坐标原点,动点
在椭圆
上,动点
满足
,记点
的轨迹为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求轨迹
的方程;
(2)在轨迹
上是否存在点
,使得过点
作椭圆
的两条切线互相垂直?若存在,求点
的坐标:若不存在,请说明理由:
(3)过点
的直线
交轨迹
于
,
两点,射线
交轨迹
于点
,射线
交椭圆
于点
,求四边形
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533b93dd6eb6b474481247736699c76c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22234a15c785f14348e5e912308b5b28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)在轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80aeea2f19e6a5b1ee6e7b5be82713ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.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/a4cfef623a9534b5708df5f95f1760a5.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/e8d4ab45e8e8f0084d8d90a4c1233d86.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
名校
解题方法
【推荐1】已知椭圆
的长轴长为4,离心率为
,过右焦点
的直线
与椭圆相交于
,
两点.
(1)求椭圆
的方程;
(2)在
轴上是否存在定点
,使得直线
,
关于
轴对称,若存在,求出
点坐标,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)在
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
名校
解题方法
【推荐2】在平面直角坐标系
中,
,
,且
满足
.记点
的轨迹为曲线
.
(1)求
的方程,并说明是什么曲线;
(2)若
,
是曲线
上的动点,且直线
过点
,问在
轴上是否存在定点
,使得
?若存在,请求出定点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852b303689c31189cd47bb4a3220f9fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53502463cc76201000e02df314e58769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437814ad18dbfb2a88865e6963ffb182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43fc91ace7f86ce3e7efbed8ead2838d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62af66af364130bfa1690702db302c75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
名校
解题方法
【推荐1】已知椭圆
的离心率为
,焦距为4.
(1)求椭圆
的方程;
(2)设过椭圆的右焦点
的动直线
与椭圆交于
、
两点(点
在
轴上方),
、
为椭圆的左、右顶点,直线
,
与
轴分别交于点
、
,
为坐标原点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过椭圆的右焦点
![](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/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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec18c028746b73be7503ff6ff458a8c.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27b957de1bf137d15eb6321b4e58f1a.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
名校
【推荐2】已知椭圆
的左右焦点为
,其离心率为
,又抛物线
在点
处的切线恰好过椭圆
的一个焦点.
(1)求椭圆
的方程;
(2)过点
斜率为
的直线
交椭圆
于
两点,直线
的斜率分别为
,是否存在常数
,使得
?若存在,求出
的值;若不存在,请说明理由.
![](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/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4754fbe523ca63eba3810a3f88f37df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f397a4a9aa5728d9fca4ca6c73789c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bcb166b53a49e393871bcb14a528792.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/0068ae8bb3fb1c75a3843e590fb30607.png)
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