名校
1 . 椭圆
的中心在坐标原点
,焦点在
轴上,椭圆
经过点
且短轴长为2.
(1)求椭圆
的标准方程:
(2)过点
且倾斜角为
的直线
与椭圆
交于A、
两点,线段
的中垂线与
轴交于点
,
是椭圆
上的一点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/8cb374fd349306abf2f784b6a28d93a7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](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/d44e8bc37ed03f44470762748a8f942a.png)
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2023-11-03更新
|
514次组卷
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2卷引用:山西省阳泉市2024届高三上学期期末数学试题
2 . 已知
为半圆
(
为参数,
)上的点,点
的坐标为
,
为坐标原点,点
在射线
上,弧
的长度为
,线段
的长为4.
(1)以
为极点,
轴的正半轴为极轴建立极坐标系,求点
的直角坐标和极坐标;
(2)求直线
的参数方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d1edafc77ae98bb8cb9aed44420773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34281318027f1d9d7cffd42d2cca8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd9e314a9d0954be3d0a7b5191b316b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14f419e14bc30fe2fada469a0fbbb64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
(1)以
![](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/ac047e91852b91af639feec23a9598b2.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
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3 . 在直角坐标系xOy中,曲线C的参数方程为
,(θ为参数).以坐标原点O为极点,x轴的非负半轴为极轴建立极坐标系,直线l的极坐标方程为
.
(1)求曲线C的普通方程和直线l的直角坐标方程;
(2)已知点P的直角坐标为
,直线l与曲线C相交于A,B两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c54fa027b03a967902077edc3ea707a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e493b78af522f00509cdfcd36b43cfd.png)
(1)求曲线C的普通方程和直线l的直角坐标方程;
(2)已知点P的直角坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86022205a7487439dd8d0897cd3bf19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3979f27823cdcba516dfa885d8afe19d.png)
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2022-05-26更新
|
855次组卷
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8卷引用:山西省忻州市第一中学校2022届高三下学期5月模拟文科数学试题
4 . 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,
轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)求
的极坐标方程;
(2)设
与
交于
两点,若
,求
的直角坐标方程.
![](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/76613bc166dc19c406b08c790f1bfecf.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/2e94bc7b8e652128e609fefd731e9b83.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b63bb6d659cfe62c412a6b04459be4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
您最近一年使用:0次
5 . 在直角坐标系
中,直线
的参数方程为
(
为参数),以原点
为极点,
轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)求直线
的极坐标方程与曲线
的直角坐标方程;
(2)直线
与曲线
交于
,
两点,求
的值.
![](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/f539d7013dc57308d676ca74575ae323.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/e2ce749ac62808d164ffc899d9871568.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)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/29cef5ef7440bb1fbb671f9c2a955497.png)
您最近一年使用:0次
2022-05-16更新
|
652次组卷
|
3卷引用:山西省运城市2022届高三下学期5月考前适应性测试数学(理)试题
名校
6 . 在平面直角坐标系
中,直线
的参数方程为
(
为参数,
),以坐标原点为极点,
轴正半轴为极轴,建立极坐标系,圆
的极坐标方程为
.
(1)求圆
的直角坐标方程;
(2)设
,若直线
与圆
相交于A,
两点,求
的最大值.
![](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/0409f7e80dcf4e42b80303530ebe193e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e4f7aa258b61c1182941521641f958c.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/ae9dd82e4a585a31335827c70c53f629.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50488f8d877acd3db584b83be7127c5.png)
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c00c8e2e2e5c6e234ca9b5193b28ca.png)
您最近一年使用:0次
2022-05-09更新
|
518次组卷
|
5卷引用:山西省晋中市2022届高三下学期5月模拟数学(文)试题
山西省晋中市2022届高三下学期5月模拟数学(文)试题山西省晋中市2022届高三下学期5月模拟数学(理科)试题山西省怀仁市第一中学校2022届高三下学期第四次模拟数学(理)试题山西省怀仁市第一中学校2022届高三下学期第四次模拟数学(文)试题(已下线)押全国卷(文科)第22题 坐标系与参数方程-备战2022年高考数学(文)临考题号押题(全国卷)
7 . 在平面直角坐标系xOy中,曲线
的参数方程为
(t为参数),以坐标原点O为极点,x轴正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)求曲线
与
的直角坐标方程;
(2)已知直线l的极坐标方程为
,直线l与曲线
,
分别交于M,N(均异于点O)两点,若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2705e3b42ae9b0941c0bb075d4e962e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0cb878349009a779d94b1bc40319bb.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)已知直线l的极坐标方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b939ad58ff2ff356d783ed2911f47ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7db98695102580eff843b6a7bb94fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2022-05-08更新
|
1578次组卷
|
17卷引用:山西省晋城市2022届高三第三次模拟文科数学试题
山西省晋城市2022届高三第三次模拟文科数学试题山西省晋城市2022届高三第三次模拟理科数学试题河南省汝州市2022届高三5月模拟考试理科数学试题吉林省白山市2022届高三模拟数学(理)试题陕西省商洛市2022届高三下学期二模理科数学试题甘肃省白银市靖远县2022届高三第三次联考数学(理)试题陕西省榆林市2022届高三下学期四模理科数学试题(已下线)押全国卷(理科)第22题 坐标系与参数方程-备战2022年高考数学(理)临考题号押题(全国卷)宁夏吴忠市吴忠中学2022届高三下学期第三次模拟测试数学(文)试题河南省汝州市2022届高三5月模拟考试文科数学试题甘肃省白银市靖远县2022届高三第三次联考数学(文)试题陕西省商洛市2022届高三下学期二模文科数学试题陕西省榆林市2022届高三下学期四模文科数学试题宁夏银川市第二中学2023届高三上学期统练三数学(理)试题新疆博乐市高级中学2021-2022学年高三下学期文科数学试题新疆博乐市高级中学2021-2022学年高三下学期理科数学试题宁夏回族自治区银川市第六中学2022-2023学年高三上学期11月月考数学试题
名校
解题方法
8 . 在平面直角坐标系中,直线的参数方程为
(
为参数).以原点
为极点,
轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)求直线
的极坐标方程和曲线
的直角坐标方程;
(2)若点
,
分别在直线
和曲线
上,且直线
的一个方向向量为
,求线段
长度的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12046073919b6c242a3bf7a4f970cc1.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/236836bd898ebf7b8d9f038851c6e071.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](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/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56dccc5720967ee3edce0174255e8ed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2022-05-07更新
|
439次组卷
|
4卷引用:山西省际名校2022届高三联考二(冲刺卷)文科数学试题
山西省际名校2022届高三联考二(冲刺卷)文科数学试题山西省际名校2022届高三联考二(冲刺卷)理科数学试题山西省太原市第五中学2022届高三下学期二模文科数学试题(已下线)押全国卷(文科)第22题 坐标系与参数方程-备战2022年高考数学(文)临考题号押题(全国卷)
名校
9 . 在直角坐标系xOy中,以坐标原点O为极点,x轴的正半轴为极轴建立极坐标系.曲线
的极坐标方程为
,将
上所有点的横坐标不变,纵坐标伸长为原来的2倍,得到曲线
.
(1)求
的直角坐标方程;
(2)已知点
,若M为
上任意一点,直线AM与
的另一个交点为N,当M为线段AN的中点时,求M的直角坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094ab3a9f3a40f6fc88a4184371dc745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e4e06c57f46c48a35f35161322a4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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2022-04-27更新
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5卷引用:山西省临汾市2022届高三三模数学(文)试题
山西省临汾市2022届高三三模数学(文)试题山西省临汾市2022届高三三模数学(理)试题(已下线)押全国卷(理科)第22题 坐标系与参数方程-备战2022年高考数学(理)临考题号押题(全国卷)江西省宜春市丰城中学2022届高三5月模拟数学(理)试题黑龙江省大庆实验中学2021-2022学年高考数学预测试题(二)理工类试题
10 . 在平面直角坐标系xOy中,曲线
的参数方程为
(
为参数),以O为极点,x轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)求曲线
的普通方程和曲线
的直角坐标方程;
(2)若点
,曲线
与曲线
的交点为A,B两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83c66e1c7a55766c4bbf9f32e6047d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c3541cbe4486b859df010c87d8b773.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33cc0f9aa168e43cc5759f017d69b498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559d66fd8b309fd440ce9bda78a579c9.png)
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6卷引用:山西省吕梁市交城县2022届高三核心模拟(下)理科数学(一)试题