1 . 在直角坐标系xOy中,曲线C的参数方程为
(其中
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,直线l的极坐标方程为
.
(1)求直线l的直角坐标方程和曲线C的普通方程;
(2)已知点
,直线l与曲线C交于M,N两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b63545dd7224e0ba29aa76f763f6da85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4f020e7f5de31b6b4967a2810b3be8.png)
(1)求直线l的直角坐标方程和曲线C的普通方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56ab70e602f2e2e291df643ab209162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82917a85af3499c0b6400b26abce2f2f.png)
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解题方法
2 . 在直角坐标系
中,曲线C的参数方程为
(a为参数),直线
的参数方程为
(t为参数).
(1)求C和
的直角坐标方程;
(2)若曲线C截直线
所得线段的中点坐标为
,求
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4590b86be57e1cddadab04f38c585621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1c85043ab723ec0e7a8655597c36b8.png)
(1)求C和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若曲线C截直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2828feafa861942ce3b395c066eb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2024-01-20更新
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2卷引用:青海省西宁市大通县2024届高三上学期期末数学(理)试题
名校
解题方法
3 . 在直角坐标系
中,直线
的参数方程为
(
为参数),直线
的参数方程为
(
为参数).
(1)求这两条直线的普通方程(结果用直线的一般式方程表示);
(2)若这两条直线与圆
都相离,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d3593494503deda8eda7690445f90fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd0b377582a468f7f45ffd3b39fd3bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
(1)求这两条直线的普通方程(结果用直线的一般式方程表示);
(2)若这两条直线与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da94e575c3747ecdcfa5896498e5cfaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-12-27更新
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6卷引用:青海省2024届高三上学期协作联考数学(理科)试题
4 . 在直角坐标系
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
的普通方程和
的直角坐标方程;
(2)若
与
相交于
两点,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/f45d252c22469137df9f2ca1489fe1d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.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/af4a0fc79d16497144efc7f070a52058.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6951479694aec937a712901634a5a4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7384b9afcef2d86a87eee0c66f383052.png)
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名校
5 . 已知倾斜角为
的直线
的参数方程为
(
为参数).在直角坐标系
中,
,以
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
.直线
与曲线
交于
两点.
(1)求
的值及曲线
的直角坐标方程;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e377a63c60132d7d7c0c22e9e950a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbcf0320d94734aedd3d4e2e31b9827.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3fdea1bdd133a14556a9612292f1c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf2d50a03130b0d6036f8354b81b7243.png)
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2023-11-29更新
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3卷引用:青海省海南藏族自治州海南州普通高中2023-2024学年高三上学期期中联考数学(理科)试题
6 . 将下列曲线的极坐标方程化为直角坐标方程.
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cf89e94eb51129f144d9809ec290f7.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e7fe7d70daba5a42a28596b1a4a498.png)
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7 . 在直角坐标系
中,圆
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,圆
的极坐标方程是
.
(1)在直角坐标系中,若直线
经过点
且与圆
和圆
的公共弦所在直线平行,求直线
的极坐标方程;
(2)若射线
与圆
的交点为
,与圆
的交点为
,线段
的中点为
,求
的周长.
![](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/8e55b035e6e99b21d1e169c03e523875.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/69cf89e94eb51129f144d9809ec290f7.png)
(1)在直角坐标系中,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69abe959988e4c8c0739f5857ccfb0f.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b5e58900c7d393263c1d420a0d99993.png)
![](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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/96d6c0b1e09f546c5ce77316daa8050f.png)
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2023-08-03更新
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4卷引用:青海省西宁市2024届高三上学期期末联考数学(文)试题
名校
解题方法
8 . 直线
(
为参数)被圆
所截得的弦长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b106b3372456901217e1b2586c3da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0ecf60aaca7da8ebd89a554ef5441f2.png)
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2023-08-01更新
|
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2卷引用:青海省西宁市七校2022-2023学年高二下学期期末联考文科数学试题
9 . 在平面直角坐标系
中,以
为极点,
轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程分别为
,
.
(1)求曲线
的直角坐标方程;
(2)若曲线
与
轴交于点
,曲线
和曲线
的交点为
,求
的值.
![](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/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c576d1667042a31f9648b26cf4c152e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f177cada8625fd80c7f6abe60b2a67.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a104774601235cc76b5f0c1683c974e1.png)
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2023-05-29更新
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4卷引用:青海省西宁市大通县2024届高三上学期开学摸底考试数学(文科)试题
名校
10 . 在直角坐标系xOy中,曲线C的参数方程为
(
为参数),以坐标原点O为极点,x轴的正半轴为极轴建立极坐标系,直线l的极坐标方程为
.
(1)求C和l的直角坐标方程;
(2)求C上的点到l距离的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/755654cb5087c4cdaf0e240319b3ffed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7ee7dce82929e9f332573b6f30e23f.png)
(1)求C和l的直角坐标方程;
(2)求C上的点到l距离的最小值.
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2023-05-18更新
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4卷引用:青海省西宁北外附属新华联外国语高级中学2022-2023学年高二下学期期末考试数学(文)试题