1 . 在直角坐标系中,直线l的参数方程为
(t为参数),以直角坐标系的原点O为极点,x轴的非负半轴为极轴建立极坐标系.在极坐标系中,曲线S的极坐标方程为
.
(1)将曲线S的极坐标方程化为参数方程;
(2)设点M的直角坐标为
,若直线l与曲线S交于A、B两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60eabfd2e3ff619c0f649a254c8bf412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0cb878349009a779d94b1bc40319bb.png)
(1)将曲线S的极坐标方程化为参数方程;
(2)设点M的直角坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/435938bc37cdc1227146afa9240ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbeb3db2d060c6261db5c7077ff62e1f.png)
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2 . 在直角坐标系中,曲线C的参数方程为
(
为参数),以坐标原点为极点,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)分别求曲线C的普通方程和直线l的直角坐标方程;
(2)已知点
,直线l与曲线C交于A,B两点,弦AB的中点为Q,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f243d740349b126e2934ab3d26ab5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76817e4d13d29c0644a6286a1f9e22ff.png)
(1)分别求曲线C的普通方程和直线l的直角坐标方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f047e7ed44a3897ec79c6c6a0c641fcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72157dd0dd502d9e3db055c62e10b736.png)
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2022-07-12更新
|
700次组卷
|
6卷引用:内蒙古赤峰市2021-2022学年高二下学期期末考试数学(文)试题
3 . 如图,在极坐标系Ox中,圆O的半径为2,半径均为1的两个半圆弧
,
所在圆的圆心分别为
,
,M是半圆弧
上的一个动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/15/9cb4724d-5baf-4ffb-8b27-0fc4e1e40cd9.png?resizew=172)
(1)当
时,求点M的极坐标;
(2)以O为坐标原点,极轴Ox为x轴正半轴,
的方向为y轴正方向建立平面直角坐标系.若点N为线段
的中点,求点N的轨迹方程.
![](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/0ac26826282f5f23f68c0c826e47e6f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4de2411cce374e702613ed54156f20a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/15/9cb4724d-5baf-4ffb-8b27-0fc4e1e40cd9.png?resizew=172)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25aa330923dd2f15ed76d442119aa92f.png)
(2)以O为坐标原点,极轴Ox为x轴正半轴,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/755330dce1f013846003b1486afe3b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f26eee4bc9133db37211e28cef00662.png)
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2022-07-12更新
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984次组卷
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9卷引用:四川省成都市2023届高三摸底测试理科数学试题
4 . 在平面直角坐标系xOy中,以原点O为极点,Ox为极轴建立极坐标系,曲线
的极坐标方程为
,曲线
的参数方程为
(t为参数).
(1)求曲线
的直角坐标方程与曲线
的普通方程;
(2)若P,Q分别为曲线
和曲线
上的动点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3d9ab4111065258254a6bdb44a4352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a187e3c547ac4b1e5bfb14bff49539.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P,Q分别为曲线
![](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/d44e8bc37ed03f44470762748a8f942a.png)
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5 . 在直角坐标系xOy中,曲线
的参数方程为
(
为参数).已知M是曲线
上的动点,将OM绕点O逆时针旋转90°得到ON.设点N的轨迹为曲线
.以坐标原点为极点,x轴正半轴为极轴建立极坐标系.
(1)求曲线
,
的极坐标方程;
(2)设点
,若射线
:
与曲线
,
分别相交于异于极点O的A,B两点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35392514850ce9e9979745b84cf321a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20242f058154f335ba691de98df4bd98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8522e2d17f61ebb76553324d7acbd8d5.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/8b17f20c25bb16153b5f2d25062ed7a7.png)
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2022-07-10更新
|
469次组卷
|
3卷引用:四川省自贡市2021-2022学年高二下学期期末考试数学(理)试题
6 . 在平面直角坐标系
中,直线
的参数方程为
(
为参数).在以原点
为极点,
轴正半轴为极轴的极坐标系中,圆
的极坐标方程为
.
(1)写出直线
的普通方程和圆
的直角坐标方程;
(2)若点
直角坐标为
,圆
与直线
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/9c8310be941f1b5a8da9726c23bd2f6b.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/4171a30d75286a3e4a1a91f31eba3c40.png)
(1)写出直线
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96394405807439f8aa1c2edd12a1d47.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3979f27823cdcba516dfa885d8afe19d.png)
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2022-07-10更新
|
337次组卷
|
2卷引用:四川省南充市2021-2022学年高二下学期期末考试数学(理)试题
7 . 已知点P的坐标为
,点Q是参数方程为
(
为参数)的椭圆C上的动点,
(1)求椭圆C的离心率;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcdf9faaba7b7c9b5973c00ef74ef212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(1)求椭圆C的离心率;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
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2022-07-09更新
|
147次组卷
|
2卷引用:广西钦州市2021-2022学年高二下学期期末考试数学(理)试题
8 . 在直角坐标系xOy中,曲线
的参数方程为
(
为参数,
,
,
).以坐标原点为极点,x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)求曲线
的普通方程和
的直角坐标方程;
(2)已知射线
与曲线
,
分别交于M,N两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35314f2c4b2cabe6583319d5b4b4c08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86f58e2cf57800ca2ae97cd347b6bc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d26c9fc8cfa002f40ea3908575c8ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e136b083dd4b00398749aa08b51ba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe6a0ff86582f9bb6aea164dbec63ce.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)已知射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50312eff223f6cc480815aad70b6855a.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/084cf5ffced059f5653ee2a1023518b7.png)
您最近一年使用:0次
9 . 在直角坐标系
中,曲线
的参数方程为
(t为参数).在以原点为极点,x轴的正半轴为极轴的极坐标系中,曲线
的极坐标方程为
.
(1)求曲线
和曲线
的直角坐标方程;
(2)设
,若曲线
与曲线
交于A,B两点,求
的值.
![](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/44d5d605a7dea88ccc8ad705c5764bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8230531720914786cf0045bb06c185.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc2de9df8bce6139613bb86322db0f4.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/9486e4e76ff07c6c47091e0e4b8bcd7d.png)
您最近一年使用:0次
2022-07-05更新
|
233次组卷
|
3卷引用:广西南宁市部分校2021-2022学年高二下学期期末联考数学(文)试题
10 . 在直角坐标系
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)写出曲线
的普通方程和曲线
的直角坐标方程;
(2)设点
的直角坐标为
,曲线
与曲线
相交于
,
两点,求
的值.
![](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/bf83c66e1c7a55766c4bbf9f32e6047d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.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/ac0d6c660bc86349c9fb43db2abc6c42.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48befa5d90fafd8bfdb6c90fd241ebfb.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e255cb6ef5a18b9e800397c55a81bf9.png)
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