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已知椭圆eqIdfd8674e21002436f9476310a52d934ec的离心率为eqIdcf32b3b919f04cc18988c622e750e9f1eqIdcc614bd3390c4d028df189b234dcc351为椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上任意一点,且已知eqIdbe11440fed7645708dc12eb7f2ad90b2.
(1)若椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的短轴长为eqIdddd35c5d043e4ebeac32a99367053c68,求eqIdad3523fb6e08473d8e9d5b211eca189a的最大值;
(2)若直线eqId6e01ec176a0c41d4b4c511e5b8adf517交椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的另一个点为eqId8754ce8cf7f34f04abb9a0c041f57f5c,直线eqId83604a8bccb74330aa114f6b5cb85f67eqId8e15963708e9415da25069fea5906e24轴于点eqId0cd8063abf2b458f80091bc51b75a904,点eqIdcc614bd3390c4d028df189b234dcc351关于直线eqId417e80f1349244878d01fe90e0891f5f对称点为eqIdc6425c23adb14cde8775c9d61fa83431,且eqIdc6425c23adb14cde8775c9d61fa83431eqId139764a4b5c8473bbc1adc1bfde324c0三点共线,求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的标准方程.
更新:2020/05/30难度:0.65题型:解答题组卷:0
已知椭圆eqIdcb94200200f74d65ac6c5aa8bd8a33d7的离心率为eqIdcf32b3b919f04cc18988c622e750e9f1,短轴的一个端点到右焦点的距离为2.
figure
(1)求椭圆eqId93cbffaa5ae045d6ac45d1e979991c3a的方程;
(2)设eqIdeb53cb7cb0274f7d8f111c60f824c243分别为椭圆eqId93cbffaa5ae045d6ac45d1e979991c3a的左、右顶点,如图,过点eqIdeb53cb7cb0274f7d8f111c60f824c243分别作直线eqIdcf2da96900c948a1b3ce7cbfd420c080eqId0627be51821d4be7b3e024a354815d64,设直线eqIdcf2da96900c948a1b3ce7cbfd420c080交椭圆eqId93cbffaa5ae045d6ac45d1e979991c3a于另一点eqId65fad45bd27b40dd981adaadbe3d6b7e交椭圆eqId93cbffaa5ae045d6ac45d1e979991c3a于另一点eqId75a143b898e14ccdb032561fba9da811,分别过eqIdcc614bd3390c4d028df189b234dcc351eqId75a143b898e14ccdb032561fba9da811作椭圆eqId93cbffaa5ae045d6ac45d1e979991c3a的两条切线,且两条切线交于点eqId7dcd2312d0bf4bb1befdfcc170e45791,分别过eqId8754ce8cf7f34f04abb9a0c041f57f5ceqIdbedf755e0fdb4d078d6859360706b163作椭圆eqId93cbffaa5ae045d6ac45d1e979991c3a的两条切线,且两条切线交于点eqId1b7d8b87b50e4cfdbf89d48980209a52.证明:点eqId19a4eb16029e4550a14f2afe4741a3c3在直线eqIdf36042897878495ba515f0ad89ae7321上.
更新:2020/05/30难度:0.4题型:解答题组卷:0
如果eqId25ff52e432b14cc6954d0c41f0e4cc3b三点在同一条直线上,那么eqId8e15963708e9415da25069fea5906e24的值是(   )
A.3B.4C.5D.6
更新:2020/05/28难度:0.94题型:单选题组卷:0
若直线eqId79da0b5117f54a47b95a492d7ecd8e0a与不等式组eqIda4cee55a468d43a3b05e64c4a25294a0表示的平面区域有公共点,则实数k的取值范围是_____.
更新:2020/05/28难度:0.65题型:填空题组卷:0
已知椭圆eqId15bfbddeee0143e08c809ecf76ffb129的左、右焦点分别为eqId5f04473e64c141bcbe9b0a8af27f4aa8eqId8bb868704ca84429be4745c5bb899ffb分别为椭圆的上、下顶点,直线eqId078a55bed08847b4b2fa537fd90d14d4与椭圆的另一个交点为D,若eqId60c0f23a44954ee68fb5477382d3fa2d,则直线eqId34c6b6e427744abfb88dc90b8c7c2111的斜率为(    )
A.eqId838fd7bdcc4e48a589a11491a13203f9B.eqIdd083af549771492d86a628c72da2a865C.eqId505792ded6474e10b78612d37a6a5727D.eqId72a10295338040499cb3747215ca8f7f
更新:2020/05/28难度:0.65题型:单选题组卷:0
已知双曲线eqId8c2bd23a7d8b4294b942371f3d924b28的左、右顶点分别为eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c,点eqIdbedf755e0fdb4d078d6859360706b163在双曲线eqId19a4eb16029e4550a14f2afe4741a3c3上,若eqId5fcb87135b7949bdafdd13aea8199864,则双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的焦距为_________.
更新:2020/05/28难度:0.85题型:填空题组卷:0
如图,已知椭圆CeqIdf18b5700afd748c9af08fbce0977010b的左、右顶点分别为eqId3ef41bfa7ab0403aaeef117199148f55右焦点为eqId53c451c54c3e474384b206f020fe3051,右准线l的方程为eqIdd59777a92d8f4da290823fc3dc6b5c26,过焦点F的直线与椭圆C相交于点AB(不与点eqId3ef41bfa7ab0403aaeef117199148f55重合).
figure
(1)求椭圆C的标准方程;
(2)当直线AB的倾斜角为45°时,求弦AB的长;
(3)设直线eqId36a204f7504d4c3a81eae2680edd9df9l于点M,求证:BeqId894f8d53415741dea8f7a841c68384d1M三点共线.
更新:2020/05/27难度:0.65题型:解答题组卷:0
设函数eqId70b0e4d861d342c88d418e51356e6861
(1)求函数eqId6f13759e937144069819aed2ae5a1057的单调区间;
(2)过坐标原点O作曲线eqId428a374a5f494c13aab87ba5ad5adbde的切线,求切点的横坐标.
更新:2020/05/26难度:0.65题型:解答题组卷:0