组卷网>高中数学综合库>平面解析几何>圆锥曲线>椭圆>椭圆的标准方程>根据a、b、c求椭圆标准方程
题型:解答题 难度:0.4 引用次数:65 更新时间:2021/1/16 22:46:04 题号:12867455
已知椭圆eqIdf18b5700afd748c9af08fbce0977010b的左右焦点分别为eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e,焦距为eqIdddd35c5d043e4ebeac32a99367053c68,直线eqId9f8986faf302481b9648e9ad0515a686与椭圆相交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,eqIdde963a24921f4ee7a991bf9d4f43a42e关于直线eqId74c7e0292b094e54ae596d37798a05ed的对称点为eqId5d8dbb36705848f0abceda756224b23a,斜率为eqIdbeffaaf8d5cd43cf8375210d69fce6be的直线eqId439fb93f7745417b8bb1747d963c6e60与线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3相交于点eqIdbedf755e0fdb4d078d6859360706b163,与椭圆相交于eqId19a4eb16029e4550a14f2afe4741a3c3eqId0cd8063abf2b458f80091bc51b75a904两点.
说明: figure
(1)求椭圆的标准方程;
(2)求四边形eqId8cb5c539b00f4c198d985dd69d29e0b5面积的取值范围.

类题推荐

解答题 | 较难(0.4) |
解题方法
【推荐1】已知椭圆eqId0bfe30d7e7ac477f871558e7fad634ab的左、右焦点分别是eqId5f04473e64c141bcbe9b0a8af27f4aa8,且离心率为eqId5f816d038c584dc7a249120298677ef3,点eqId2381423d4cd146cab95f55527681a766为椭圆下上动点,eqId9c85ce533b3f4c73a1913f2b3c5d58e1面积的最大值为eqId37705e1ef6a84bbdbe88433e75932cdf
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的标准方程;
(2)若eqId2381423d4cd146cab95f55527681a766是椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的上顶点,直线eqId17ab120dd1484145a133e6a409c8465c交椭圆eqId19a4eb16029e4550a14f2afe4741a3c3于点eqId517584fed25c413ba8b7bb33ffa2d5c6,过点eqId0aa72756ed0c4c7a89f26aa94f43e47d的直线eqId417e80f1349244878d01fe90e0891f5f(直线eqId417e80f1349244878d01fe90e0891f5f的斜率不为1)与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3交于eqIdad5a3fe6c747453488b22964c985d62c两点,点eqIdbedf755e0fdb4d078d6859360706b163在点eqId75a143b898e14ccdb032561fba9da811的上方.若eqIde7274e4dd55d46a2bac601b297a1ffd6,求直线eqId417e80f1349244878d01fe90e0891f5f的方程.
更新:2020/12/03组卷:978
解答题 | 较难(0.4) |
解题方法
压轴
【推荐2】已知椭圆eqId76662bc293df4139b90c65ed8b136d3b(eqIde9c1eda3dc0c4304868ea148d833743f)的上顶点为eqId93cbffaa5ae045d6ac45d1e979991c3a,左焦点为eqId63db14a5b4334f3ea583c8fb12b0d175,离心率为eqId5f816d038c584dc7a249120298677ef3,直线eqId1a0830891ff846de8422ea80714ecab4与圆eqIdfb5d832b1a4f453dac65ee1949f03c35相切.
说明: figure
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的标准方程;
(2)设过点eqId63db14a5b4334f3ea583c8fb12b0d175且斜率存在的直线eqId417e80f1349244878d01fe90e0891f5f与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3相交于eqIdeb53cb7cb0274f7d8f111c60f824c243两点,线段eqIdeb53cb7cb0274f7d8f111c60f824c243的垂直平分线交eqId8e15963708e9415da25069fea5906e24轴于点eqIdbedf755e0fdb4d078d6859360706b163,试判断eqId2926f8665407409c9bd1fa2d28a0b96d是否为定值?并说明理由.
更新:2020/02/19组卷:558
解答题 | 较难(0.4) |
典型
【推荐3】已知椭圆eqId9bb644ac30a84dc1b7017a6bf4ccf189的离心率为eqIdd1ebfa5c81a04d18900d19595d070677,一个焦点在直线eqId7f0e23129ca140fe8f9412605ce33b60上,直线eqId417e80f1349244878d01fe90e0891f5f与椭圆交于eqId6ad3b2a9811545558a564b0085d94cc4两点,其中直线eqIda668e52822264c18a05bbdd44d38eb84的斜率为eqIdd4bf9298f0db4fb5afb67e0d739f3074,直线eqId7101cb5936ef49d7bb72d9e58960606c的斜率为eqId75fdb198d83447e59e31c1f4923cc3bc
(1)求椭圆方程;
(2)若eqId1fbb27b85901493ea774f9bcdd7b64fd,试问⊿eqId01148cae2a4e4a18b560a52866799f29的面积是否为定值,若是求出这个定值,若不是请说明理由。
更新:2019/07/16组卷:1381
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