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1 . 多样化的体育场地会为学生们提供更丰富的身体锻炼方式.现有一个标准的铅球场地如图,若场地边界曲线M分别由由两段同心圆弧
和两条线段
四部分组成,在极坐标系
中,
,A、O、B三点共线.
,点C在半径为1的圆上.
(2)若需设置一个距边界曲线M距离不小于1且关于极轴所在直线对称的矩形警示区域,如图,求警示区域所围的最小面积.
注:
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4947600808d89be0f44ee44184245904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea0e1899670d6a143a225256c59348f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918a29dde19360105c62d3842fbac0e7.png)
(2)若需设置一个距边界曲线M距离不小于1且关于极轴所在直线对称的矩形警示区域,如图,求警示区域所围的最小面积.
注:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf1671d3e1e5e9c394d738e8d6f12e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77e18f18ddcd6bc68867f8eb76930e37.png)
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2022-04-14更新
|
732次组卷
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6卷引用: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)
(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)四川省泸县第二中学、泸县二中实验学校2022届高三上学期模拟考试数学(文)试题(已下线)四川省成都市第七中学2024届高三上学期期末数学(理)试题四川省成都市第七中学2024届高三上学期期末数学(文)试题四川省成都市成华区某校2023-2024学年高三下学期“三诊”数学(理)试题四川省成都市成华区某校2023-2024学年高三“三诊”数学(文)试题
名校
解题方法
2 . 过点
作斜率为
的直线交椭圆
于
两点,若
上存在相异的两点
使得
,则
外接圆半径的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797c488729678e74e0825c2e92b544b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/680a5a5c24751e0e37ee306308465faf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e88ab2f7f0cc281e62fbc7e920e0cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2ef94a9b287291939e463b5a7c7ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96645a3530e72d5d733d2c72147d340.png)
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3 . 如图,曲线
是著名的笛卡尔心形曲线,它的极坐标方程为
.曲线
是经过极点且在极轴上方的圆,其圆心在经过极点且垂直于极轴的直线上,直径为1.
![](https://img.xkw.com/dksih/QBM/2022/3/16/2937582708613120/2938453271224320/STEM/61775c10c76044e8833986d81c4bd063.png?resizew=191)
(1)求曲线
的极坐标方程,并求曲线
和曲线
交点的极坐标;
(2)以极点为坐标原点,极轴所在的直线为x轴,经过极点且垂直于极轴的直线为y轴,建立平面直角坐标系,曲线
的参数方程为
(t为参数).若曲线
与曲线
相交于除极点外的M,N两点,求线段MN的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb60128f02b8c4d2454eb5ba062c3f8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://img.xkw.com/dksih/QBM/2022/3/16/2937582708613120/2938453271224320/STEM/61775c10c76044e8833986d81c4bd063.png?resizew=191)
(1)求曲线
![](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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)以极点为坐标原点,极轴所在的直线为x轴,经过极点且垂直于极轴的直线为y轴,建立平面直角坐标系,曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d90d85e0a401b070ea2fd6d6f6d1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
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2022-03-18更新
|
1600次组卷
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6卷引用: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)
(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)(已下线)考向45坐标系与参数方程(重点)-1四川省成都市实验外国语学校2021-2022学年高二下学期第一次阶段性考试数学(文)试题四川省眉山第一中学2022届高考适应性考试数学(理)试题甘肃省2022届高三下学期第一次高考诊断考试理科数学试题甘肃省2022届高三下学期第一次高考诊断数学(文)试题
21-22高二·全国·课后作业
4 . 在数轴上,对坐标分别为
和
的两点A和B,用绝对值定义两点间的距离,表示为
.
(1)在数轴上任意取三点A,B,C,证明
.
(2)设A和B两点的坐标分别为
和2,分别找出(1)中不等式等号成立和等号不成立时点C的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7a1a35fb8112b8b0661c9e5281839dd.png)
(1)在数轴上任意取三点A,B,C,证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bcaabd563b35f69c5059c8d4e71a98.png)
(2)设A和B两点的坐标分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
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5 . 已知
是双曲线
的左右焦点,
为圆
上一动点(纵坐标不为零),直线
分别交两条渐近线于
两点,则线段
中点的轨迹为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b9e1820afc1d893b071b97b3c99b09e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/830dae557581905657626ad99f536b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25d82387e48eafb286785a21a8d4150f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
A.平行直线 | B.圆的一部分 |
C.椭圆的一部分 | D.双曲线的一部分 |
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2022·上海·模拟预测
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解题方法
6 . 在椭圆
中,直线
上有两点C、D (C点在第一象限),左顶点为A,下顶点为B,右焦点为F.
(1)若∠AFB
,求椭圆
的标准方程;
(2)若点C的纵坐标为2,点D的纵坐标为1,则BC与AD的交点是否在椭圆上?请说明理由;
(3)已知直线BC与椭圆
相交于点P,直线AD与椭圆
相交于点Q,若P与Q关于原点对称,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0740d5e3f81ae7822f9598ebd4c463e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d61b78d69cfd82cf0d69792c977dc0.png)
(1)若∠AFB
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ab912a775d000596215001d1331184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)若点C的纵坐标为2,点D的纵坐标为1,则BC与AD的交点是否在椭圆上?请说明理由;
(3)已知直线BC与椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b24b94392a78a2325a4834c2018a8e2f.png)
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7 . 已知点
、
的极坐标为
、
,直线
经过
、
两点,曲线
的极坐标方程为
,直线
与曲线
相交于
、
两点. 以极点为坐标原点,极轴为
轴的正半轴,建立平面直角坐标系
.
(1)求直线
的极坐标方程和曲线
的参数方程;
(2)求
.
![](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/171532ccbe6889c0532ac7d9fd99ff4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5517b9a8b9ec47d6ddd48a961a38e8ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cda90ec15c07139032c7fed43bcc385.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
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2021-12-15更新
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708次组卷
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3卷引用:专题28 极坐标与参数方程解答题20题-备战2022年高考数学冲刺横向强化精练精讲
8 . 如图,在极坐标系
中,正方形
的边长为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd0caec008c15302ca973b8e655b748.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/9e438ea4-5afe-4ddb-a414-4c0bb6bef0c2.png?resizew=199)
(1)求正方形
的边
的极坐标方程;
(2)若以
为原点,
分别为轴,
轴正方向建立平面直角坐标系,曲线E:
与边BC,CD分别交于点
Q,求直线
的参数方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab158dd9e96abcae0f115f54fa66c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd0caec008c15302ca973b8e655b748.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/9e438ea4-5afe-4ddb-a414-4c0bb6bef0c2.png?resizew=199)
(1)求正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab158dd9e96abcae0f115f54fa66c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481e426224c3a3ce9bb5a731eed81c40.png)
(2)若以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79e77ce349def2476f60d0349d445dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d35465f3e40ce00a1dce54b943ae183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8fbc229c957487495bb8cda1d4cfd8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
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2021-12-09更新
|
788次组卷
|
5卷引用:专题28 极坐标与参数方程解答题20题-备战2022年高考数学冲刺横向强化精练精讲
(已下线)专题28 极坐标与参数方程解答题20题-备战2022年高考数学冲刺横向强化精练精讲四川省泸州市2021-2022学高三第一次教学质量诊断性考试数学(理)试题四川省泸州市2021-2022学年高三第一次教学质量诊断性考试数学(文)试题四川省宜宾市第四中学2022届高三二诊模拟考试数学(理)试题四川省宜宾市第四中学2022届高三二诊模拟考试数学(文)试题
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9 . 已知圆O:x2+y2=2,过点A(1,1)的直线交圆O所得的弦长为
,且与x轴的交点为双曲线E:
=1的右焦点F(c,0)(c>2),双曲线E的离心率为
.
(1)求双曲线E的方程;
(2)若直线y=kx+m(k<0,k≠﹣
,m>0)交y轴于点P,交x轴于点Q,交双曲线右支于点M,N两点,当满足关系
时,求实数m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f2ea8fcb101c2ecba2b2c862eb66b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
(1)求双曲线E的方程;
(2)若直线y=kx+m(k<0,k≠﹣
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/398dc09164ba83d47d2d3a9af3ad4312.png)
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10 . 已知直线
:
(
为参数).
(1)当
时,求直线
的斜率;
(2)若
是圆
:
内部一点,
与圆
交于
、
两点,且
,
,
成等比数列,求动点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a106912c62d48bddb8f9c4eb4c126d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3416881a6f67d05fe6b67787047fc86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827539d066d1b78e7ef8bc1569864971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d063ec7f9dbeba72fabf4437f9400e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f645d4b09fba53f971172cd2602c691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ce8eed2660a33465a7f764e76cdba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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