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题型:解答题 难度系数:0.65 引用次数:142 更新时间:2019/01/11 03:43:58 题号:7446559
已知椭圆以坐标原点为中心,焦点在轴上,焦距为2,且经过点.
(1)求椭圆的方程;
(2)设点,点为曲线上任一点,求点到点距离的最大值
(3)在(2)的条件下,当时,设的面积为O是坐标原点,Q是曲线C上横坐标为a的点),以为边长的正方形的面积为,若正数满足,问是否存在最小值,若存在,请求出此最小值,若不存在,请说明理由.
类题推荐
【推荐1】已知椭圆eqId2bb51f84ac224dc2abe1e4b2122e8cb5的离心率为eqIdd19abe37f2d8471e8da802d66c25862c,左、右焦点分别为eqIdadf5adeb3ae644dc89c819829df0a901eqId0cfe24caa0fc44de8e0fcd142d6c1377eqIdcc614bd3390c4d028df189b234dcc351为相圆eqId19a4eb16029e4550a14f2afe4741a3c3上一点,eqId2f17701fd3fb4101b1bab39270ac6de4eqId072d7d6b911b42bc89207e72515ebf5f轴交于eqId8754ce8cf7f34f04abb9a0c041f57f5ceqIde07e97174f6d438f84df9d6e0e8ff24aeqId95ed2d49095b481690aeba5399a6a017.
figure
(Ⅰ)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(Ⅱ)过右焦点eqId0cfe24caa0fc44de8e0fcd142d6c1377的直线eqIdf1d65a8dc5bf45bd8cdb4a1d694df672交椭圆于eqIdd7be5abad1e34f6db17a56660de8d54feqIdca9308a4ebd84ed8a28d8a519a8dbb39两点若eqId4ea1af672e334fb1a6a3ab675d494e72的中点为eqId8eea7f6267fb49d9bce12b8ba079a43eeqIdaad7b72a25924d078d2360cdc99f1090为原点,直线eqId8566fa87c9b048e2876317573b8fb1ef交直线eqIdd1aa6979d2324054b68c4f097fb400f3于点eqId2381423d4cd146cab95f55527681a766.求eqId45b8c1c3cf6c4c929a9b35b68bc21594的最大值.
难度系数:0.85使用:71次题型:解答题更新:2019/6/17
【推荐2】椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId15bfbddeee0143e08c809ecf76ffb129,其长轴是短轴的两倍,以某短轴顶点和长轴顶点为端点的线段作为直径的圆的周长为eqId4706510f15104e3097f4c0d908df4157,直线eqId417e80f1349244878d01fe90e0891f5f与椭圆交于eqId3219ed8963724a0ba02478d8233e822deqIde1eed0fa858947c080db4beefde041c6两点.
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)过点eqIdaad7b72a25924d078d2360cdc99f1090作直线eqId417e80f1349244878d01fe90e0891f5f的垂线,垂足为eqId0cd8063abf2b458f80091bc51b75a904.若eqId2bbf701dd40d44099a6877b791bb9306,求点eqId0cd8063abf2b458f80091bc51b75a904的轨迹方程;
(3)设直线eqIdbb9a819299654135a84936d08d832c73eqId417e80f1349244878d01fe90e0891f5feqIdbdb9b3ab33a542d9b1aefcf002989543的斜率分别为eqIdd4bf9298f0db4fb5afb67e0d739f3074eqId4d2187284c5d4de29906363f7d21f60feqId75fdb198d83447e59e31c1f4923cc3bc,其中eqId4f5682ff18d8421ab17ef168f54ca081eqIde60bd9c2d55c4d57bb16d37e8544a143.设eqId25f18a3e6b1f49ff919fe1bee7f02bd7的面积为eqId1b7d8b87b50e4cfdbf89d48980209a52.以eqIdbb9a819299654135a84936d08d832c73eqIdbdb9b3ab33a542d9b1aefcf002989543为直径的圆的面积分别为eqIde0b0a69153d74086acac0f2b28878deceqIdc36de5c6d722440e9911d9802c4068f8,求eqId35af45a25f454746bfbcce97ffac9e6b的取值范围.
难度系数:0.4使用:46次题型:解答题更新:2019/6/20
【推荐3】已知椭圆eqId15bfbddeee0143e08c809ecf76ffb129eqId6f417c44c1e74c8a89ca068bfe3595a7是长轴的一个端点,弦eqId0627be51821d4be7b3e024a354815d64过椭圆的中心eqIdaad7b72a25924d078d2360cdc99f1090,点eqId19a4eb16029e4550a14f2afe4741a3c3在第一象限,且eqId3de530473397495594412e99eb886370eqIdb0fe0a0d18284426bea9d9961deab75c
(1)求椭圆的标准方程;
(2)设eqIdd7be5abad1e34f6db17a56660de8d54feqIdca9308a4ebd84ed8a28d8a519a8dbb39为椭圆上不重合的两点且异于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c,若eqId8c4027f6519c466db4f97b4da87671f8的平分线总是垂直于eqIdc12aac8c2448479687a40735b3572a23轴,问是否存在实数eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c,使得eqIda8f7ca06d36a4614a7e74a263b72afcf?若不存在,请说明理由;若存在,求eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c取得最大值时的eqId4ea1af672e334fb1a6a3ab675d494e72的长.
难度系数:0.65使用:50次题型:解答题更新:2019/6/21
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