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1 . 已知直线eqIdcb408cdb9cd04b05bef100061f2c1430t为参数),曲线eqIdf691fdb4529a438aa01bf89b3da55acc
(1)求直线eqIdcfc8599bedfb4ab4944abf141f348a9a的普通方程与曲线eqId3a63d00111554b9e8b896929779a293d的直角坐标方程;
(2)求直线eqIdcfc8599bedfb4ab4944abf141f348a9a被曲线eqId3a63d00111554b9e8b896929779a293d所截得的弦长.
2 . 已知圆eqId2381423d4cd146cab95f55527681a766经过两点eqId05a3f9e9557247efa1715adb34924696eqId1bc6a7035a14433e88e51e3f675fd17c且圆心eqId2381423d4cd146cab95f55527681a766在直线eqIdfe7f11d0668e4772b48510adb9ba20d4上.
(1)求圆eqId2381423d4cd146cab95f55527681a766的方程;
(2)设eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175是圆eqId2381423d4cd146cab95f55527681a766上异于原点eqId2efda802d5534f6d92d9f8af7aaec28b的两点,直线eqId3bb73d6153b04891a6c74abe379306b9eqIdf7c24389743c4a5bbf4e1284fcd400c8的斜率分别为eqIdd4bf9298f0db4fb5afb67e0d739f3074eqId75fdb198d83447e59e31c1f4923cc3bc,且eqIdda94f73622324316b4e927a18dcf52cb,求证:直线eqId1a0830891ff846de8422ea80714ecab4经过一定点,并求出该定点的坐标.
解答题 | 一般(0.65) | 2021·江苏高考真题
解题方法
3 . 已知函数eqId4837c94ef0ff4dcf9b1dda4df363275a是定义在eqIdfe6a989a623d4e69bd402eb92f4aae25上的偶函数,当eqId4db620a5946b4ee0a9f530f35a6d505a时,eqId2b43ce1f825a4545a59591f3cfd5b972(eqId982da3835b7946d999cc8604a2ece266,且eqIdd951487aa2c84adebbd85d63425e0e52).又直线eqIda70b517c44da4bada5d0392c028eea12恒过定点A,且点A在函数eqId4837c94ef0ff4dcf9b1dda4df363275a的图像上.
(1) 求实数eqId70a27b6ddf6b478285353abb3b1f3741的值;
(2) 求eqIdb484c8b29a654705b3db583c080f64d0的值;
(3) 求函数eqId4837c94ef0ff4dcf9b1dda4df363275a的解析式.
单选题 | 较易(0.85) | 2021·浙江绍兴市·高二期末
解题方法
4 . 以直线eqId0bb537f247614d4f8d353c45d36cab6d经过的定点为圆心,2为半径的圆的方程是(   )
A.eqId9394b88854f74479a0a67e1a305043d8B.eqIdedd23ce21c8c45049f3142085b8eaf6d
C.eqId245b06b526014e92826ec6dfd6b37066D.eqIdab53159fb01f422d8449fb7ebe263f96
5 . “曼哈顿距离”是十九世纪的赫尔曼eqId88a9c3b9656848269672503e1df8507f闵可夫斯基所创辞汇,定义如下:在直角坐标平面上任意两点eqId7d297dfa4ab24bfdbfadb3a392221a8aeqId31762c4ae4564a1c88243ab8035e7813eqIda52ddfa59b924e8b98cae0093d8dbdf7的曼哈顿距离为:eqIde0b5de785ba0443d983102aa098b8ef8.在此定义下以下结论正确的是(   )
A.已知点eqIdaf9281434a074809a72d5741f0f69745,满足eqIde6cb9a2bbfbd47188fe9c01cc1293e5d的点eqId2381423d4cd146cab95f55527681a766轨迹围成的图形面积为2
B.已知点eqId4fa41502eca04f1a95316e6a3b9a3a0aeqId01ff06e70b6f4bbb879db937ff2aece6,满足eqId4f4683871c2c44e2b38502731e726f22eqIdf8db943844104afaa0934b2fd8d6cd92eqIdd5f25720a4f242eb859be3f3011de518的点eqId2381423d4cd146cab95f55527681a766轨迹的形状为六边形
C.已知点eqId4fa41502eca04f1a95316e6a3b9a3a0aeqId01ff06e70b6f4bbb879db937ff2aece6,不存在动点eqId2381423d4cd146cab95f55527681a766满足方程:eqId3e618deae86c49b1896bd1fbe5e9d644eqId943bc2f6388143a593ef4c6549c3ab81eqId311d38dfcbbe4ddc8c1dd7a781407078
D.已知点eqId2381423d4cd146cab95f55527681a766在圆eqId8fe6478b722549e99756201e8fb01d41上,点eqId517584fed25c413ba8b7bb33ffa2d5c6在直线eqId2bda3c050f7a42bfb87eb5b903a3edb3上,则eqId4f4683871c2c44e2b38502731e726f22eqIdfc29bef2d9274839b3a1c155dbd40c11的最小值为eqIdebafe25f72bf49f994542063cf580969
解答题 | 一般(0.65) | 2021·贵州遵义市·高二期末(理)
6 . 已知eqId7749df1ac7bf4efb8aa86872dab999bb圆心在直线eqIdb545805bdae44bc4b4d7e1264caead7f上,且过点eqIddf6ff38451f04add900431590850c424eqId9347243351c040689b450d371e74f4f8
(1)求eqId7749df1ac7bf4efb8aa86872dab999bb的标准方程;
(2)已知过点eqId0a91a135fedc49b9a4a15e2784ba3810的直线eqId417e80f1349244878d01fe90e0891f5f被所截得的弦长为4,求直线eqId417e80f1349244878d01fe90e0891f5f的方程.
单选题 | 较易(0.85) | 2021·贵州遵义市·高二期末(理)
解题方法
7 . 直线eqIddaa81c391480450b8a339927c8d9daec过定点(   )
A.eqIdff343dc03adf4062b1306213897b270eB.eqIdaa72ba402c544faebf55fcec7b01baf2C.eqIddc687105e60b4f238747cc880e416835D.eqIdba0328e4f5fb46e4b72de87f55321196
单选题 | 较易(0.85) | 2021·广西河池市·高二期末(文)
解题方法
8 . 已知斜率为eqIdbeffaaf8d5cd43cf8375210d69fce6be的直线eqId417e80f1349244878d01fe90e0891f5f被圆eqId19a4eb16029e4550a14f2afe4741a3c3eqIdae3d4095f09d454c9a104d423e4e4a92截得的弦长为eqId807b61b62f09462994e31cf497210538,则直线eqId417e80f1349244878d01fe90e0891f5f的方程为(   )
A.eqId7ef234275e784efaae5217eccc9a7f0eeqIdbd2c8e6823a44ae5af525275c4523ccf
B.eqId1642e65278b14670b8d166488392b92feqId41af6300a6614fe3beee0146eb3c7e96
C.eqId10377b4dea7042b48d34dfb46c9beab6eqIde5fcb1d98dab480e9ef83a2e7ceaa0b4
D.eqIda14da2618dc04897956ab9abc800a93ceqId14a346e8d395488aad2bc51987f8fbad
9 . (1)求经过点eqId82537fdd3eea4572b1ce70941de33977,点eqId55d2276dc69a457babd491d85ad87a04,且圆心在直线eqId762500ba8ef1409c9131f0f2fd5091ac上的圆的方程;
(2)已知圆eqId19a4eb16029e4550a14f2afe4741a3c3上的点eqId366040149ff640f385d54b009a9c6f29关于直线eqId177c047ef4a54a738707545fff93dae8的对称点仍在圆eqId19a4eb16029e4550a14f2afe4741a3c3上,圆eqId19a4eb16029e4550a14f2afe4741a3c3的面积为eqIda0aba3c9a8dd4a4cac52ba27bcd80753,圆心eqId19a4eb16029e4550a14f2afe4741a3c3在第二象限,且直线eqId312e64547fa244caafa4bb8b9fe657bb与圆eqId19a4eb16029e4550a14f2afe4741a3c3相交于eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175两点,求eqIdbab9b685a75b4fea966282b699e18edf
10 . 已知四边形eqId5ce7a06ae7a34393b92b5277978ac014是平行四边形,eqId3ce7665100834dddab52d1a8c2881473eqIda45750ccb9654816b6f9a1545b71e2dceqId75b12c8d6499453db27356f9478d4e78 ,且eqId93cbffaa5ae045d6ac45d1e979991c3a为线段eqId34c6b6e427744abfb88dc90b8c7c2111的中点.
(1)求线段eqId34c6b6e427744abfb88dc90b8c7c2111的垂直平分线eqId74c7e0292b094e54ae596d37798a05ed的方程;
(2)直线eqId439fb93f7745417b8bb1747d963c6e60经过点eqId0cd8063abf2b458f80091bc51b75a904,且eqIdb0ab6a14fc704522a3cc95dc055a9523,求eqId439fb93f7745417b8bb1747d963c6e60eqId072d7d6b911b42bc89207e72515ebf5f轴上的截距.
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