1 . [选修4—4:坐标系与参数方程]
在平面直角坐标系
中,曲线
的参数方程为
(
为参数,
),以坐标原点
为极点,
轴的非负半轴为极轴,建立极坐标系,直线
的极坐标方程为
.
(1)设
是曲线
上的一个动点,当
时,求点
到直线
的距离的最小值;
(2)若曲线
上所有的点都在直线
的右下方,求实数
的取值范围.
在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbaf9fa94e2d0be33952022a5070e18d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b3cacc24c7cd34a4a7c20292ad5382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95227443b8ea51f1a5c7eec8feabffa9.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7fa79a550591eb9e1bd07bced3a08fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
2 .
,
是
:
上两个动点,且
,
,
到直线
:
的距离分别为
,
,则
的最大值是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ff5c21185c13eae675906dabd3593c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895fa47a776962dd68b3ff39812cad9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a4b32d388558eb9a9e4f0f2dd57c09.png)
A.3 | B.4 | C.5 | D.6 |
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3 . 已知α,β,γ为平面,
是直线,若α∩β=
,则“α⊥γ,β⊥γ”是“
⊥γ”的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
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4 . 若不等式
与关于x不等式
<0的解集相同,则
=_____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72e5270cf018e6ce7c9e944327a41be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ded083c8614b6c4b1bb605245e1b37c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a507c062709cfe2f218896247461c7d3.png)
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5 . 在直角坐标系中(
为坐标原点),已知两点
,
,且三角形
的内切圆为圆
,从圆
外一点
向圆引切线
,
为切点.
(1)求圆
的标准方程.
(2)已知点
,且
,试判断点
是否总在某一定直线
上,若是,求出直线
的方程;若不是,请说明理由.
(3)已知点
在圆
上运动,求
的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97644e932dc3e6dae8d709ac724bea10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b73867537316afdd8a452334222a6e7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a44aa6beb0b8948618d252e7b765de6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291aaad429837ab6dc1f99b9f7327cf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d134204485637cd6bda21c8853df3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5672321564c8d4f9ee1efeeccf6ae1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbf37abf427d4fff377d378e1562a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/702922399a38f03d6e397c94522b918b.png)
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6 . 设
为坐标原点),若
三点共线,则
的最小值是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/340b7fe1b2002a7a7fbda4647ee39b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3470f8e8142a61cfd3d4aa1e1e203d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd0e2c2932bd0292c4e2e5627c7496b.png)
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7 . 在直角坐标系
中,直线
的参数方程为
,(
为参数),在以原点
为极点,
轴的正半轴为极轴的极坐标系中,曲线
的极坐标方程为
.
(Ⅰ)直接写出直线
、曲线
的直角坐标方程;
(Ⅱ)设曲线
上的点到与直线
的距离为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79735f122ff526dbf7b628e5e4eafde0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd1b1be7372f241aa953201f0342d44.png)
(Ⅰ)直接写出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)设曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
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四川省宜宾市叙州区第一中学校2022-2023学年高三下学期开学考试数学(理)试题四川省宜宾市叙州区第一中学校2022-2023学年高三下学期开学考试数学(文)试题2016届云南省高三下学期第一次高中毕业生复习统一测试理科数学试卷2016届云南省高三下学期第一次高中毕业生复习统一测试文科数学试卷江西省南昌市东湖区第十中学2019-2020学年高三上学期期中数学(文)试题江西省南昌市东湖区第十中学2019-2020学年高三上学期期中数学(理)试题河南省实验中学2019-2020学年高三上学期期中数学试题江西省丰城市第九中学2020届高三上学期期中考试数学(理)试题江西省丰城市第九中学2020届高三上学期期中考试数学(文)试题内蒙古赤峰二中2021届高三上学期第二次月考数学(文科)试题陕西省渭南市临渭区2021届高三下学期二模理科数学试题陕西省渭南市临渭区2021届高三下学期二模文科数学试题
2014·湖南·二模
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解题方法
8 . 已知
都是定义在R上的函数,
,且
且
,
,对于有穷数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56db2947acc1b434ac4e436a7a805567.png)
,任取正整数
,则前
项和大于
的概率是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7efb7959737b85f732106ede7426f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5437c07cf95807f26b38be4fad6b740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990641ac6a3b81cfa4fc0c86e84c6a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56db2947acc1b434ac4e436a7a805567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5218090bb899f069ba65e5b8090cb13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c910a13b3b0dbd8fb94cfff132dd11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb10f418620f7be1f8c7e94fb0b7a0fb.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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