1 . 在直角坐标系
中,已知倾斜角为
的直线
过点
,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
,直线
与曲线
分别交于
、
两点.
(1)写出直线
的参数方程和曲线
的直角坐标方程;
(2)若
,求直线
的斜率
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c179fe7eff7abfdd092b63c9c1b82d0c.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/bcdebedd02b4ea57f8562443742086d3.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5715c31128080205f4ed35dd2721a160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
2 . 已知极点与坐标原点
重合,极轴与
轴非负半轴重合,
是曲线
上任一点
满足
,设点
的轨迹为
.
(1)求曲线
的平面直角坐标方程;
(2)将曲线
向右平移
个单位后得到曲线
,设曲线
与直线
(
为参数)相交于
、
两点,记点
,求
.
![](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/20a70a6c0f59170633dee377e5ea2149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc77d0721190ca91579169ffed7ef75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)将曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c62e79ae9d40d5ca6fe81aba1ad2074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.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/c3627350f7d2ef1a7fb62343407719d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa9491bc6dbc25914cf3abcd136d34d.png)
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2020-01-04更新
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2卷引用:四川省成都市树德中学2019-2020学年高三11月阶段性检测数学(文)试题
名校
3 . 在直角坐标系
中,曲线C的参数方程为
为参数.在以原点
为极点,为参数).在以原点
为极点,轴的正半轴为极轴的极坐标系中,直线
的极坐标方程为
.
(Ⅰ)求曲线C的普通方程和直线
的直角坐标方程;
(Ⅱ)设
,直线
与曲线C交于M,N两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4349a992a8f98854b795a4507ddbba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82fadf70ebb6e85063dacc1367d11d63.png)
(Ⅰ)求曲线C的普通方程和直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c179fe7eff7abfdd092b63c9c1b82d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7922050b92aaa9af6abf24f01fb4b23.png)
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2019-09-12更新
|
883次组卷
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6卷引用:四川省宜宾市叙州区第二中学校2019-2020学年高三下学期第二次月考数学(理)试题
4 . 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
.
(Ⅰ)分别写出直线
的普通方程与曲线
的直角坐标方程;
(Ⅱ)已知点
,直线
与曲线
相交于
,
两点,若
,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/1e84c886d1cd7ff5356a532568bb33c7.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/2d894ed1efa15dd135795e9f273b61c3.png)
(Ⅰ)分别写出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879080beb1e55cae2639645cd64c4710.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/af8a814b1cd636b0ec03d7c592b7b7d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2019-03-22更新
|
1108次组卷
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2卷引用:2019届四川省成都石室中学二诊模拟数学文科试卷
名校
5 . 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,
轴正半轴为极轴建立极坐标系,直线
的极坐标方程为
.
(1)求直线
与曲线
公共点的极坐标;
(2)设过点
的直线
交曲线
于
,
两点,且
的中点为
,求直线
的斜率.
![](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/70e824858b43372250cc404df221e708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c7afba7fa24b295454141892a5a986.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc210625e54a64a625eaa3dbf841c9f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
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2019-01-28更新
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7卷引用:【全国百强校】四川省成都外国语2018-2019学年高二5月月考文科数学试题
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解题方法
6 . 已知曲线C的极坐标方程是ρsin2θ-8cosθ=0.以极点为平面直角坐标系的原点,极轴为x轴的正半轴,建立平面直角坐标系xOy.在直角坐标系中,倾斜角为α的直线l过点P(2,0).
(1)写出曲线C的直角坐标方程和直线l的参数方程;
(2)设点Q与点G的极坐标分别为
,(2,π),若直线l经过点Q
,且与曲线C相交于A,B两点,求△GAB的面积.
(1)写出曲线C的直角坐标方程和直线l的参数方程;
(2)设点Q与点G的极坐标分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c22b1e5f86598a830d503d0746f81d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c22b1e5f86598a830d503d0746f81d.png)
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2019-08-16更新
|
752次组卷
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6卷引用:四川省双流中学2016-2017学年高二下学期6月月考数学试题
名校
7 . 在平面直角坐标系
中,直线
的参数方程是
(
为参数),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
,且直线
与曲线
交于
,
两点
(1)求曲线
的普通方程及直线
恒过的定点
的坐标;
(2)在(1)的条件下,若
,求直线
的普通方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f024643162579f252bb8dbf944ba9f0f.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/81c47c1f7715852bd00b722d78999378.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)求曲线
![](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)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae873bd8d1d3b8f94fabbdcaf18ca46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2019-01-07更新
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2卷引用:【全国百强校】四川外语学院重庆第二外国语学校2017届高三下学期第二次检测数学(文)试题