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2 . 在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的方程为eqIddfe56a07c22a44e09767c3e16dc14481,直线eqId417e80f1349244878d01fe90e0891f5f的参数方程为eqId2231e1ea08bc42ed94b586a9b5d6f469eqId32454977564e4ee18da36bd51156c509为参数),若将曲线eqIdcfc8599bedfb4ab4944abf141f348a9a上的点的横坐标不变,纵坐标变为原来的eqId767acf51abfd4d97a757561d1a882151倍,得曲线eqId3a63d00111554b9e8b896929779a293d
(1)写出曲线eqId3a63d00111554b9e8b896929779a293d的参数方程;
(2)设点eqIdbe11440fed7645708dc12eb7f2ad90b2,直线eqId417e80f1349244878d01fe90e0891f5f与曲线eqId3a63d00111554b9e8b896929779a293d的两个交点分别为eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6,求eqId548930ef1e0b4028b2fcde22946f220a的值.
3 . 已知函数eqIdce2a763a47394ca48377323dd947ff56,其中eqId7b5559fa52604169ac0cb99796b61142表示不大于eqId8e15963708e9415da25069fea5906e24的最大整数(如eqIdcece23187ac7486b81258bb022a8b6bceqId7a5301cb23d04a00adb4cf6aff849a9e),则函数eqId4837c94ef0ff4dcf9b1dda4df363275a的零点个数是(   )
A.4B.3C.2D.1
解答题 | 一般(0.65) | 2019·桂梧高中高二月考(文)
解题方法
4 . 把总长为20m的篱笆围成一个矩形场地
(1)设一边长为xm,求矩形场地的面积(用x的代数式表示面积);
(2)求矩形场地的最大面积.
6 . 在极坐标系中,射线eqId6aca159c17834faaa18eefb6c33582b7与圆eqId4aa0b05f22eb440eaba215ee1ee5c445交于点eqIdcc614bd3390c4d028df189b234dcc351,椭圆eqIdbf31c16f10784d76851cf83e57c2eeed的方程为eqId26874feca9704f42bc3a60c175ac9204,以极点为原点,极轴为eqId8e15963708e9415da25069fea5906e24轴正半轴建立平面直角坐标系eqId2272a344734c4fb088737b84294f7219
(1)求点eqIdcc614bd3390c4d028df189b234dcc351的直角坐标和椭圆eqIdbf31c16f10784d76851cf83e57c2eeed的参数方程;
(2)若eqId93cbffaa5ae045d6ac45d1e979991c3a为椭圆eqIdbf31c16f10784d76851cf83e57c2eeed的下顶点,eqId63db14a5b4334f3ea583c8fb12b0d175为椭圆eqIdbf31c16f10784d76851cf83e57c2eeed上任意一点,求eqIdcfeae0924123406cb4d159fa90acfd59的取值范围
解答题 | 一般(0.65) | 2019·贵州高三期末(理)
8 . 在直角坐标系xOy中,以坐标原点O为极点,以x轴正半轴为极轴建立极坐标系,曲线C的极坐标方程为ρ2﹣4ρsinθeqIdd3a5f4837d8d46e6aec7f9868c4a6707)=0.
(1)求曲线C的直角坐标方程;
(2)若直线l的参数方程是eqId5f7682f8368e45cba6d4cc365a9e9573α为参数),且α∈(eqId512e96e99a214eb2954a9cae4d6a230d,π)时,直线l与曲线C有且只有一个交点P,求点P的极径.
9 . 在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,直线eqId417e80f1349244878d01fe90e0891f5f的参数方程为eqId2d51f35f035d471c91f94d6d03e6946b(其中eqId69f56ef2c88b4b73a560da59f5247a82为参数,且eqIdbb688f4a0e66409a94d4468844510d27,在以eqId2efda802d5534f6d92d9f8af7aaec28b为极点、eqIda9cd3f94eb8045438f75e9daccfa7200轴的非负半轴为极轴的极坐标系(两种坐标系取相同的单位长度)中,曲线eqId19a4eb16029e4550a14f2afe4741a3c3的极坐标方程为eqIdaa0ec4c4ad9b480588ad21ad9c2ed533,设直线eqId417e80f1349244878d01fe90e0891f5f经过定点eqIdbedf755e0fdb4d078d6859360706b163,且与曲线eqId19a4eb16029e4550a14f2afe4741a3c3交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点.
(Ⅰ)求点eqIdbedf755e0fdb4d078d6859360706b163的直角坐标及曲线eqId19a4eb16029e4550a14f2afe4741a3c3的直角坐标方程;
(Ⅱ)求证:不论eqId70a27b6ddf6b478285353abb3b1f3741为何值时,eqId29a61501cae94882a602867d4953ed51为定值.
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