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单选题 | 较易(0.85) | 2022·全国高三专题练习
解题方法
1 . 椭圆eqId151b9ffdb39e46a1908d87aa0e9ecc47的焦点为F1F2,点P为椭圆上一动点,当∠F1PF2为钝角时,点P的横坐标的取值范围是(   )
A.eqId3f806ff4b6ea43f9b545cb65cfa4be03B.eqId8b07b8eae1a0470cbb55436862b3d89e
C.eqId067fae4281c0415fbe12c2ca15e453e6D.eqId7a2ea49e2a314d30a0ae6baecbc4ead6
更新:2021/09/15组卷:0
填空题 | 较难(0.4) | 2022·全国高三专题练习
解题方法
2 . 如图,已知椭圆eqId3ef1b747a7b146abb22f9ef5e723e5f9y2=1的左焦点为FO为坐标原点,设过点F且不与坐标轴垂直的直线交椭圆于AB两点,线段AB的垂直平分线与x轴交于点G,则点G横坐标的取值范围为________
说明: figure
更新:2021/09/15组卷:0
解答题 | 较难(0.4) | 2022·全国高三专题练习
3 . 椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId16914fec33714679ad51c8be8849392f的左、右焦点分别是eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e离心率为eqIde4d58f42bad9461b93d451da718fc6f4,过eqId0aa72756ed0c4c7a89f26aa94f43e47d且垂直于eqIda9cd3f94eb8045438f75e9daccfa7200轴的直线被椭圆eqId19a4eb16029e4550a14f2afe4741a3c3截得的线段长为1.
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)点eqIdbedf755e0fdb4d078d6859360706b163是椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上除长轴端点外的任一点,连接eqId837ff378f14241e39d932f0cc9ac064deqIdf95334ee237f468eb6f7b97d394bd72d,设eqId2d613c3320f749928aa15e77efdd2969的角平分线eqId47a318d9b1764ea2a94d27059e48c3a6eqId19a4eb16029e4550a14f2afe4741a3c3的长轴于点eqId03bc711b53314f76a2d3a68b21517789,求eqIda4be99d332154d13a4a6ed1ff6444fe7的取值范围;
更新:2021/09/15组卷:0
单选题 | 一般(0.65) | 2022·全国高三专题练习
解题方法
4 . 已知椭圆Cx2eqId6243cf782cd448a2949d1ceca1ddde7d=1(b>0,且b≠1)与直线lyxm交于MN两点,B为上顶点.若BMBN,则椭圆C的离心率的取值范围是(   )
A.eqIda0bff2dcadcf4ce9b82cd6580c32f002B.eqIdc93ce9b7d99447bda122e260643e615e
C.eqId54dfc17d1f37428284e472bb3479b10eD.eqId6e1e7555cd0842d3834a09c21c6fcc65
更新:2021/09/15组卷:0
解题方法
压轴
5 . 曲线eqId19a4eb16029e4550a14f2afe4741a3c3是平面内与两个定点eqId21c66a21613149768160b9b26fdec9a3eqId72dba7a4b7b4442d8226a6b7f579aa21的距离之积等于eqId16fc2c4ac7e940cdad49c4a01d735579的点的轨迹,则下列结论正确的有(   )
A.曲线eqId19a4eb16029e4550a14f2afe4741a3c3过坐标原点对称
B.曲线eqId19a4eb16029e4550a14f2afe4741a3c3关于坐标轴对称
C.若点eqIdbedf755e0fdb4d078d6859360706b163在曲线eqId19a4eb16029e4550a14f2afe4741a3c3上,则eqId91b5afff2e5c47d29221db654954eb15的周长有最小值eqId62503849440740cf8754af7e844ba72c
D.若点eqIdbedf755e0fdb4d078d6859360706b163在曲线eqId19a4eb16029e4550a14f2afe4741a3c3上,则eqId91b5afff2e5c47d29221db654954eb15的面积有最大值eqId89403f52fdd44d509ce3d76afa22965f
单选题 | 一般(0.65) | 2021·河南高三开学考试(文)
解题方法
6 . 已知过eqId4a2f65e28a2f4af590fed5fc63a93c36的直线与抛物线eqId504043705c7b469984c7c6225a08dc3f交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,eqId2381423d4cd146cab95f55527681a766为弦eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点,eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,直线eqIdb948d8e112cd4a0f996872a13421359b与抛物线的另一个交点为eqId517584fed25c413ba8b7bb33ffa2d5c6,则两点eqId517584fed25c413ba8b7bb33ffa2d5c6eqId2381423d4cd146cab95f55527681a766纵坐标的比值范围是(   )
A.eqIdcb79cfbd0e8a43b49fc80ab6ff77de1cB.eqIdd3554667d85845cb9563f0f5e017bdf8
C.eqIdc5380acaa2864ba5a831e0e9184dfee9D.eqId9f709cdc29384938b095f88a442129c2
解答题 | 较难(0.4) | 2021·江北区·重庆十八中高二月考
解题方法
压轴
7 . 如图,已知椭圆eqId67d7e6a1b6a14162b19d420842844e13,抛物线eqId35e35b29b2d447f2977063d12aa792ee,点eqId052844cae8574a8ab842c38a039baac0是椭圆eqIdcfc8599bedfb4ab4944abf141f348a9a与抛物线eqId3a63d00111554b9e8b896929779a293d的交点,过点eqId052844cae8574a8ab842c38a039baac0的直线eqId417e80f1349244878d01fe90e0891f5f交椭圆eqIdcfc8599bedfb4ab4944abf141f348a9a于点eqId8754ce8cf7f34f04abb9a0c041f57f5c,交抛物线eqId3a63d00111554b9e8b896929779a293d于点eqId2381423d4cd146cab95f55527681a766eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId2381423d4cd146cab95f55527681a766不同于eqId052844cae8574a8ab842c38a039baac0).
说明: figure
(1)求椭圆eqIdcfc8599bedfb4ab4944abf141f348a9a的焦距;
(2)设抛物线eqId3a63d00111554b9e8b896929779a293d的焦点为eqId63db14a5b4334f3ea583c8fb12b0d175eqIdbedf755e0fdb4d078d6859360706b163为抛物线上的点,且eqId052844cae8574a8ab842c38a039baac0eqId63db14a5b4334f3ea583c8fb12b0d175eqIdbedf755e0fdb4d078d6859360706b163三点共线,若存在不过原点的直线eqId417e80f1349244878d01fe90e0891f5f使eqId2381423d4cd146cab95f55527681a766为线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点,求eqId05ec8252b3694b51916dbd7b343da503的最小值.
解答题 | 一般(0.65) | 2021·陕西西安市·西安中学(理)
解题方法
8 . 已知抛物线eqIdc4f921dd48614d8391f44e52eb5bda1d的焦点为eqId63db14a5b4334f3ea583c8fb12b0d175,若过点eqId63db14a5b4334f3ea583c8fb12b0d175且倾斜角为eqIdeacabdda233342049ddc066b54feb1fe的直线交抛物线eqIdbf31c16f10784d76851cf83e57c2eeedeqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6两点,满足eqIdb658601b8df34637bfac7d19873719cb.
(1)求抛物线eqIdbf31c16f10784d76851cf83e57c2eeed的方程;
(2)过点eqIda1cd10f53ea0476d8a9f38220978c001且斜率为1的直线被抛物线eqIdbf31c16f10784d76851cf83e57c2eeed截得的弦为eqId99a3187c2b8f4bcc9703c74c3b72f1f3,若点eqId63db14a5b4334f3ea583c8fb12b0d175在以eqId99a3187c2b8f4bcc9703c74c3b72f1f3为直径的圆内,求eqIda4be99d332154d13a4a6ed1ff6444fe7的取值范围.
解答题 | 一般(0.65) | 2021·济宁市育才中学高二开学考试
解题方法
9 . 已知动点eqIdbedf755e0fdb4d078d6859360706b163在椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqIdd448b721bc2f41f8bed63e9521739ce3eqId207ddd75d0ee42629ce30bec7dcdaba1)上,eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e为椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的左、右焦点.过点eqIdbedf755e0fdb4d078d6859360706b163eqIda9cd3f94eb8045438f75e9daccfa7200轴的垂线,垂足为eqId7c79ef7a09ce49e2982f71813ff9deef,点eqId13c3876e30a7487b817853539dc875df满足eqId852d992f6a204f7fb7637c2cc82a9802,且点eqId13c3876e30a7487b817853539dc875df的轨迹是过点eqIda54c47a8f4d547e48528c05ad4481d89的圆.
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)过点eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e分别作平行直线eqId74c7e0292b094e54ae596d37798a05edeqId439fb93f7745417b8bb1747d963c6e60,设eqId74c7e0292b094e54ae596d37798a05ed交椭圆eqId19a4eb16029e4550a14f2afe4741a3c3于点eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId439fb93f7745417b8bb1747d963c6e60交椭圆eqId19a4eb16029e4550a14f2afe4741a3c3于点eqId312ef2c826304089b9b0f1d1e88b0f50eqId93cbffaa5ae045d6ac45d1e979991c3a,求四边形eqId3b970dd712b24810ac8d4cfcb34f5fe8的面积的最大值.
双空题 | 一般(0.65) | 2021·东城区·北京二中高三月考
解题方法
10 . 动点eqIdbedf755e0fdb4d078d6859360706b163与给定的边长为1的正方形在同一平面内,设此正方形的顶点为eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3eqId312ef2c826304089b9b0f1d1e88b0f50(逆时针方向),且eqIdbedf755e0fdb4d078d6859360706b163点到eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3的距离分别为eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqId44925af6fb19413689ba5616e3647cba.若eqIdef90a66d754645a6b720c8c7b8a99572,则点eqIdbedf755e0fdb4d078d6859360706b163的轨迹是________eqIdbedf755e0fdb4d078d6859360706b163点到eqId312ef2c826304089b9b0f1d1e88b0f50点的最大距离为________