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已知抛物线eqId91d153665f12451bb66d663cf54c2b6a的焦点为eqIdd5b10b2a13f148b78e0d5a1b820538fd,若过点eqIdd5b10b2a13f148b78e0d5a1b820538fd且斜率为1的直线与抛物线相交于eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6两点,且eqIdb658601b8df34637bfac7d19873719cb.
(1)求抛物线eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)设直线eqIde6451cfbccd740149989ae7519227fff,且在eqId072d7d6b911b42bc89207e72515ebf5f轴上的截距为2,eqIdfc3da0d522324433b7d5fb46712ec757与抛物线交于eqId06e60c1a2261437ba646a9bc18a212b1eqId92869ac114124367b45f631d030ed6bd两点,求eqId1c9600be89be4095a64f92457b06b0ef面积.
更新:2019/12/11难度系数:0.65题型:解答题组卷:0次
如图,四边形eqId5ce7a06ae7a34393b92b5277978ac014为正方形,eqId43fe05c727b14343a0211870697669c9平面eqId5ce7a06ae7a34393b92b5277978ac014eqId0c33e6bbacf04a76833d6f0e6bc80d34eqId6f652d3703414e188c68ad08a6ecbe55.
figure
(1)证明:eqId965c491c3a984b3fbd04afdf9e3dbb59平面eqId1461bf2a622a48cd885e5c7bd6592266
(2)证明:eqId6c1e85e16eb64f3890e8ae1223aed385平面eqIdee45356a5f324b4090ea9e68b7c0b08e
更新:2019/12/11难度系数:0.65题型:解答题组卷:0次
已知中心在坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b的椭圆eqId19a4eb16029e4550a14f2afe4741a3c3经过点eqIdbd3d7bc26c584f2482139bafba798f57,且点eqIda9a6893a743340ba93c1a9b5bdfd5309为其右焦点.
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)直线eqId417e80f1349244878d01fe90e0891f5f平行于直线eqIdbb9a819299654135a84936d08d832c73,且过点eqId9dcf523375b44757af564a5d6c40a55f,若直线eqId417e80f1349244878d01fe90e0891f5f与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3有公共点,求eqId32454977564e4ee18da36bd51156c509的取值范围.
更新:2019/12/11难度系数:0.85题型:解答题组卷:0次
过椭圆eqIdd72db2c50e834738a5c19a35835e717e内一点eqId29080c91a1b44f30aa5d9bc21982c0f4引一条弦,使弦被点eqId2381423d4cd146cab95f55527681a766平分,求这条弦所在的直线方程______.
更新:2019/12/11难度系数:0.85题型:填空题组卷:0次
已知eqIdd5b10b2a13f148b78e0d5a1b820538fd是双曲线eqId7a2471ded4b440b3bc89d38b5743e77c的右焦点,eqIdd7be5abad1e34f6db17a56660de8d54feqId19a4eb16029e4550a14f2afe4741a3c3左支上一点,eqIdc431679153cd49b5ae9e22c321526e38,当eqId87a4c4bf19364ca99fd7b3697704cdf8周长最小时,该三角形的面积为(   )
A.eqIdcb0b4d348f474513aaf4718b21559f01B.eqIdc80535ff5ba3497faa5ad47a53fb96a8C.eqIdff25aec330ed43bf9a08c748bf94f8b8D.eqIdec106e1cee0e42d7b774c593a7591ca8
更新:2019/12/11难度系数:0.65题型:单选题组卷:0次
正四棱锥eqIddd5f333edd7c4a01b271754239943f8d中,eqId9d62af31961b4590b8304cb2ab25a75e,则直线eqIdcf2da96900c948a1b3ce7cbfd420c080与平面eqIde499a0d7181a4bf4bfcd70c68255bab7所成角的正弦值为(   )
A.eqIda1b78c9af44346ddb4d164e485b4b8a7B.eqIdd90d42b6b616485585b2c5a5bd194eb6C.eqId18c57999a18a435b8420e97c41639876D.eqIde0b8cd3018f64415bea8dce0a25d0538
更新:2019/12/11难度系数:0.94题型:单选题组卷:0次
已知eqIdd7be5abad1e34f6db17a56660de8d54f为抛物线eqIdd050af449075401299cc78c647d310e8上一个动点,eqId75a143b898e14ccdb032561fba9da811为圆eqId574e6481bfc443eebda9b228005f6760上一个动点,那么点eqIdd7be5abad1e34f6db17a56660de8d54f到点eqId75a143b898e14ccdb032561fba9da811的距离与点eqIdd7be5abad1e34f6db17a56660de8d54f到抛物线的准线距离之和的最小值是(   )
A.5B.8C.eqIdc01441b4cb0f4d0098661ef17174a31cD.eqIde5a4ff398f02492b8b6986b6b2444b71
更新:2019/12/11难度系数:0.85题型:单选题组卷:0次
如图所示,在平行六面体eqId588284d93dc5489295f8f224f8e30d13中,设eqIdbfab0ef5168f41bdbb728e5b12aae456eqId28c349c443de4229bb72e56bcad7d80deqId47a0ba4e3e0a451991d7d2047e7ce1afeqId517584fed25c413ba8b7bb33ffa2d5c6eqId0627be51821d4be7b3e024a354815d64的中点,试用eqIdf087b35a5011425daaafbf14a5e61064eqId5f16eb46594d47b58ffc973b5cc2dd0deqIdfe72fe3d77e34f6e89f18aeb25a9a009表示eqIdf3a692f9fc0b463681f421062ebc1354(   )
figure
A.eqId195379a7883e476a83174b8d3afa1b9dB.eqIda2b7309b4c654d34b21b01a561ce906dC.eqIdd6959fb8584c4256851bd6e1b8ce2843D.eqId00d60a720d3b488eb55bc5e76b27b18d
更新:2019/12/11难度系数:0.94题型:单选题组卷:0次
某家具厂生产一种办公桌,每张办公桌的成本为100元,出厂单价为160元,该厂为鼓励销售商多订购,决定一次订购量超过100张时,每超过一张,这批订购的全部办公桌出厂单价降低1元.根据市场调查,销售商一次订购量不会超过160张.
(1)设一次订购量为eqId8e15963708e9415da25069fea5906e24张,办公桌的实际出厂单价为eqIdd7be5abad1e34f6db17a56660de8d54f元,求eqIdd7be5abad1e34f6db17a56660de8d54f关于eqId8e15963708e9415da25069fea5906e24的函数关系式eqId51fc5baa718e4bc0a260ae58f86521e4
(2)当一次性订购量eqId8e15963708e9415da25069fea5906e24为多少时,该家具厂这次销售办公桌所获得的利润eqId4837c94ef0ff4dcf9b1dda4df363275a最大?其最大利润是多少元?(该家具厂出售一张办公桌的利润=实际出厂单价-成本)
更新:2019/12/10难度系数:0.85题型:解答题组卷:11次
已知eqId4837c94ef0ff4dcf9b1dda4df363275a是定义在eqId7dcd2312d0bf4bb1befdfcc170e45791的奇函数,当eqId26126945e23544d9b0cecaf9cf4809ac时,eqId9a05e5148d6a458f9c2ec3aab81d1976.若函数eqId4837c94ef0ff4dcf9b1dda4df363275aeqId47bb553718a644a9aba68733ad08312a上单调递减.
(1)求eqId70a27b6ddf6b478285353abb3b1f3741的取值范围;
(2)若对实数eqId410ed18ec7d441cea651f48851f8e361eqId5947419403914ed5a9fab009957215b5 恒成立,求实数eqId32454977564e4ee18da36bd51156c509的取值范围.
更新:2019/12/10难度系数:0.65题型:解答题组卷:20次
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