组卷网>高中数学综合库>平面解析几何>圆锥曲线>椭圆>椭圆的定义>利用椭圆定义求方程
题型:解答题 难度:0.4 引用次数:670 更新时间:2020/9/29 19:31:37 题号:6631831
已知椭圆C:eqIdf18b5700afd748c9af08fbce0977010b经过点eqId4f6423021a9942349bf59b74930037a1, eqId5f04473e64c141bcbe9b0a8af27f4aa8是椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的两个焦点,eqId50c60c33445b4139bddc85aeb0465c38eqIdbedf755e0fdb4d078d6859360706b163是椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上的一个动点.
(1)求椭圆说明: figure的标准方程;
(2)若点说明: figure在第一象限,且eqId101b5e1caff842d1ae3aba8b4fba446f,求点说明: figure的横坐标的取值范围;

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解答题 | 较难(0.4) |
【推荐1】在平面直角坐标系xOy中,已知椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId15bfbddeee0143e08c809ecf76ffb129的左,右焦点分别为eqIddb3c03d9220648818a7719d8c214e52feqId92b9e9e1d00e4ed0b16fbbb1e4df224a.点eqId37008431a281465a90fe13efe1cb76aa是椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId8e15963708e9415da25069fea5906e24轴上方的动点,且△eqIda92d58b10653408fa6707249995ea6d2的周长为16.  

figure

(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)设点eqIdca9308a4ebd84ed8a28d8a519a8dbb39到△eqIda92d58b10653408fa6707249995ea6d2三边的距离均相等.
①当eqId788b63d3d4de4aaf8770731533c84bef时,求点eqIdca9308a4ebd84ed8a28d8a519a8dbb39的坐标;
②求证:点eqIdca9308a4ebd84ed8a28d8a519a8dbb39在定椭圆上.
更新:2017/07/26组卷:478
解答题 | 较难(0.4) |
解题方法
【推荐2】eqId7431d070400e4b3c9f15d6551249c176eqId4adb29c41ef646e2b946ad55cc5bdd5deqIdaf43e4850d21410dafa81fbb082c3881为直角坐标平面内eqIda9cd3f94eb8045438f75e9daccfa7200eqId072d7d6b911b42bc89207e72515ebf5f轴正方向上的单位向量,若向量eqId14cca796d41d42878fcacf27ff1e1ce9eqIdb73416c2cb5340fa8dd25d507dc2f636,且eqId6822ad0d4a5c4ce49d5c9dcfbe241ea8.
(1)求点eqId9eadb467bb044d669030fbe083ff2b2f的轨迹eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)过点eqId71f9948507e842958823524c2980d790作直线eqId417e80f1349244878d01fe90e0891f5f与曲线eqId19a4eb16029e4550a14f2afe4741a3c3交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,设eqId52882604ab224858a6bb833e18c8944c,是否存在这样的直线eqId417e80f1349244878d01fe90e0891f5f,使得四边形eqId41d8decac91e40f897bf90a51926a253是矩形?若存在求出直线eqId417e80f1349244878d01fe90e0891f5f的方程;若不存在,试说明理由.
更新:2020/06/26组卷:85
解答题 | 较难(0.4) |
解题方法
【推荐3】在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,点eqIdeaa090972d1c4331be045bec87b5edcb,圆eqIdde963a24921f4ee7a991bf9d4f43a42eeqIdf2668f8f36ad4a999153b5c9b76dc355,点Q是圆上一动点,线段eqId99a03a3d5e6e45e9b084760ef1ceaf50的中垂线与线段eqId7a91b507da1b4f2b856efc2a25bbbda7交于点说明: figure.
(1)求动点P的轨迹P的方程;
(2)设直线l经过点eqId21f035c64d0e44c8b3b944b13f27fe68且与C交于不同的两点MN,试问:在轴上是否存在点G,使得直线eqId52025b5068c44b1fae0b81843b7d103b与直线eqId469d1f048aa34268b364e4f94c349898的斜率的和为定值?若存在,求出点G的坐标及定值;若不存在,请说明理由.
更新:2020/12/30组卷:28
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