名校
1 . 在直角坐标系
中,直线
的参数方程为
(
为参数),曲线
的参数方程为
(
为参数),以该直角坐标系的原点
为极点,
轴的非负半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)分别求曲线
的极坐标方程和曲线
的直角坐标方程;
(2)设直线
交曲线
于
,
两点,交曲线
于
,
两点,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157f62a2e90eb2cabcda5d7fe09562d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abd09af119941fa000c5dd85d6f2e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b40ec2b25361a0ddce73fc4b13750dd6.png)
(1)分别求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
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2019-01-22更新
|
5089次组卷
|
16卷引用:【市级联考】福建省宁德市 2019届高三第一学期期末质量检测数学理科试题
【市级联考】福建省宁德市 2019届高三第一学期期末质量检测数学理科试题【市级联考】福建省宁德市2019届高三第一学期期末质量检测数学文科试题【市级联考】四川省乐山市2019届高三第三次调查研究考试数学(文)试题【市级联考】四川省乐山市高中2019届高三第三次调查研究考试数学理试题江西省景德镇一中2018-2019学年高二下学期期中考试数学(文)试题四川省绵阳市涪城区南山中学2019-2020学年高三上学期11月月考数学(理)试题陕西省渭南市2019-2020学年高三上学期期末数学文科试题2020届陕西省渭南市高三上学期期末(一模)数学(理)试题甘肃省民乐县第一中学2019-2020学年高三3月线上考试数学(理)试题(已下线)理科数学-2020年高考押题预测卷02(新课标Ⅰ卷)《2020年高考押题预测卷》(已下线)专题14 坐标系与参数方程-2020年高三数学(理)3-4月模拟试题汇编(已下线)理科数学-2020年高考押题预测卷03(新课标Ⅱ卷)《2020年高考押题预测卷》(已下线)文科数学-2020年高考押题预测卷03(新课标Ⅱ卷)《2020年高考押题预测卷》东北三省四市教研联合体2021届高三第二次联合考试理科数学试题东北三省三校(哈师大附中、辽宁省实验中学、东北师范大学附属中学)2021届高三二模数学(理)试题河南省中原名校联盟2021-2022学年高三下学期3月适应性联考文科数学试题
名校
2 . 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),曲线
的参数方程为
(
为参数),在以
为极点,
轴的正半轴为极轴的极坐标系中,射线
与
各有一个交点,当
时,这两个交点间的距离为2,当
时,这两个交点重合.
(1)分别说明
是什么曲线,并求
与
的值;
(2)设当
时,
与
的交点分别为
,当
时,
与
的交点分别为
,求直线
的极坐标方程.
在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe534877fd5af3f860d841818cd0cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b680d16a2061ec17ed29c18caf37d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b81f058a7887e19f2a03bb1a13847d.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/dc35770ab113e9d9ce8f8fc53c3271e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51cc689a7ccf4acfd2d5ecba23e9768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc316f251b316a8a62c60017289cc80.png)
(1)分别说明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)设当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4120436d6ff0c58109473edc068257c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8454989732716850cb57ca15f8ef596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5d90872781fa4c870c01378e6925fea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ee712dfc82e1acc31ef8dcad479a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ef38914882dc88fcd98c468d08d59d.png)
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名校
3 . 在平面直角坐标系
中,以坐标原点
为极点,
轴正半轴为极轴建立极坐标系,已知曲线
的极坐标方程为:
,直线
的参数方程是
(
为参数,
)
(Ⅰ)求曲线
的直角坐标方程;
(Ⅱ)设直线
与曲线
交于两点
,
,且线段
的中点为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/6b996d5790cb49cacbc409b8b2e8e3b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be52e351ecceca327b99934365714a6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10adc3992efb2badc23f81d36faa206f.png)
(Ⅰ)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cda12642d59a5817e8990c43de20535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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2017-03-20更新
|
4262次组卷
|
9卷引用:2017届陕西省咸阳市高三二模数学(理)试卷
4 . 在直角坐标系
中,以原点
为极点,
轴的正半轴为极轴建立极坐标系.已知曲线
(
为参数),
(
为参数).
(1)将
的方程化为普通方程,并说明它们分别表示什么曲线;
(2)若
上的点
对应的参数为
,
为
上的动点,求
中点
到直线
:
的距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/e440e99c23198ba33e53ae3ee327598b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d1a34ae2b8c77f8d7e355c6d1d667e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae806d9529ba7eb19805c9625198f508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ab55147ca5c0f958af43b0637ee31b.png)
(1)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c797f498399b8dc1d9826ef988e4b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4866650805ac11a464ad1e54c091a3.png)
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