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1 . 在直角坐标系eqId2272a344734c4fb088737b84294f7219中,曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的参数方程为eqId9524e69d0a2d4ad385096e79493ee5f3(eqId69f56ef2c88b4b73a560da59f5247a82为参数).以eqId2efda802d5534f6d92d9f8af7aaec28b为极点,eqIda9cd3f94eb8045438f75e9daccfa7200轴正半轴为极轴建立极坐标系,曲线eqId3a63d00111554b9e8b896929779a293d的极坐标方程为eqId6eb90e6dd0ff4effa0bfa2a98eba9b9c.
(1)求曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的极坐标方程;
(2)若曲线eqIdcfc8599bedfb4ab4944abf141f348a9a上有且仅有两个点到曲线eqId3a63d00111554b9e8b896929779a293d的距离为eqId37705e1ef6a84bbdbe88433e75932cdf,求eqIdaea992e70d4943e49e893817eb885ed7的取值范围.
2 . 在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的参数方程为eqIdcaf8cf6851b04dbbae33bc93027a0f2eeqIdc13953f2514e4c8f9c8aaaf5241c33ac为参数且eqIde8263436cfdf4c6b84fb160604c0f268),以坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b为极点,eqIda9cd3f94eb8045438f75e9daccfa7200轴的正半轴为极轴建立极坐标系,曲线eqId3a63d00111554b9e8b896929779a293d的极坐标方程为eqId2efe850d2fab419e8897701227743021
(1)说明eqIdcfc8599bedfb4ab4944abf141f348a9a是哪种曲线,并将eqIdcfc8599bedfb4ab4944abf141f348a9a的方程化为极坐标方程;
(2)设点eqId052844cae8574a8ab842c38a039baac0的极坐标为eqId83ee1bdf01354ca4b0d9c1eaf09447a5,射线eqId542af876313745359038036fdd480f01eqIdcfc8599bedfb4ab4944abf141f348a9a的交点为eqId2381423d4cd146cab95f55527681a766(异于极点),与eqId3a63d00111554b9e8b896929779a293d的交点为eqId517584fed25c413ba8b7bb33ffa2d5c6(异于极点),若eqId2a6a75aa47dd485bb83d0efe2c9419d9,求eqId3405c14024ad4c0cbe6501af458a45fb的值.
解答题 | 较易(0.85) | 2020·安徽高三月考(理)
解题方法
3 . 在极坐标系中,已知eqIdb5d5aa2aaaf4449ab90eebd2b7681bea在直线eqId417e80f1349244878d01fe90e0891f5feqIde6c10f921eb14d428880db7b54a6494b上,点eqIde906d0b5978c494a94630760d518f315在圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId2efe850d2fab419e8897701227743021上(其中eqIdff70c420e5e24ab6bd7925626be5c251eqIda59404b32a47432f87bd315cc2167998).
(1)求eqId4819509fefec4542acccfcf3d67cd699
(2)求出直线eqId417e80f1349244878d01fe90e0891f5f与圆eqId19a4eb16029e4550a14f2afe4741a3c3的公共点的极坐标.
4 . 如图,在平面直角坐标系中,以坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b为极点,eqIda9cd3f94eb8045438f75e9daccfa7200轴的正半轴为极轴建立极坐标系eqId5b17d7c502534fbaaff7f0ae4db5c73d,极坐标系中eqIdf34fda17b58046de9229f5bd96df2589eqId1f8f31a2b3e045d7b8c299429dff1f23eqId2f41884fe84245afa7f2745f20f55ea0eqIdef47bf2e2e664843bfae483cffb23fb7,弧eqIdb9deff7870114ad2a9c2900096c4e734所在圆的圆心分别为eqIde6ee4da1498d478fa5c522f011db824aeqIddbb3302d2bfa446b9361aabc343daf2ceqIdf75936022e374464abaf8ababd62f1baeqId510e7ec518ff4e57886e36249011c3a3,曲线eqIdcfc8599bedfb4ab4944abf141f348a9a是弧eqId1609e6778d084a1d9bb2bf4111fcf29a,曲线eqId3a63d00111554b9e8b896929779a293d是弧eqIde9e20ea2b5e0416483dfd1b21da92040,曲线eqId32ece98e0955476591d5f4a55111a471是弧eqIde29dca1dc76b42e791635f885e7ea97d,曲线eqIdfe5fafb7eaf1405fa89e2790180767f6是弧eqId36ab7a2c986f4e2cbb02eaa4db59c0bf.
说明: figure
(1)分别写出eqId9fb8bb4e24c246af8474d519333b98bd的极坐标方程;
(2)直线eqId417e80f1349244878d01fe90e0891f5f的参数方程为eqIde5f22445add34cd0b052a12fc1655104eqId69f56ef2c88b4b73a560da59f5247a82为参数),若直线eqId417e80f1349244878d01fe90e0891f5f与曲线eqIdcfc8599bedfb4ab4944abf141f348a9a有两个不同交点eqId71891062a8724584af9a2c4c77cd566e,求实数eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c的取值范围.
解答题 | 一般(0.65) | 2020·全国高二课时练习
6 . 在长方体eqId588284d93dc5489295f8f224f8e30d13中,eqIde2f8bc21e65f476d8e4dfb6bcc9ed5f0eqIdfe737ff044dd42c1bba7c0bd71ecb93beqIdc0ccc58b8e954a0a83b879635b3538b8,E为eqIdf12c98a2bca444d1bc8a7dbd264d9955的中点.
说明: figure
(1)求直线eqIda17165d2b65e424e95b04e5ef7b21e8deqId30ace6b4ce264294a0534221c1b01e26所成角的余弦值;
(2)若FBC的中点,求直线eqIda17165d2b65e424e95b04e5ef7b21e8d与平面eqId1e4738125ec74a99be88f6c7469a5175所成角的正弦值.
7 . 在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,直线eqId417e80f1349244878d01fe90e0891f5f的参数方程为eqId48cbf22315c84804b3429d7ec49869f7eqId69f56ef2c88b4b73a560da59f5247a82为参数).以原点为极点,eqIda9cd3f94eb8045438f75e9daccfa7200轴正半轴为极轴建立极坐标系,曲线eqId19a4eb16029e4550a14f2afe4741a3c3的极坐标方程为eqId275ce029abf94fd5ba3147f907cfe7d2.直线eqId417e80f1349244878d01fe90e0891f5f与曲线eqId19a4eb16029e4550a14f2afe4741a3c3有两个不同的交点eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c
(Ⅰ)求eqId70a27b6ddf6b478285353abb3b1f3741的取值范围;
(Ⅱ)若eqId316e2199840e418e87252dba1d7d7ffdeqId4c33bf068751457396f330d902841106,求eqId604da716be7d4b6ab4fc882abb0ca582的值.
解答题 | 容易(0.94) | 2020·浙江高二单元测试
解题方法
同步
9 . 已知不等式组eqIdaed2ec479b7845a789ca7086fc585f3c
(1)画出不等式组所表示的平面区域(要求尺规作图,不用写出作图步骤,画草图不能得分);
(2)求平面区域的面积.
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