1 . 已知曲线
的参数方程为
(
为参数),曲线
的直角坐标方程为
.以原点O为极点,x轴的正半轴为极轴建立极坐标系.
(1)求曲线
和
的极坐标方程;
(2)若直线l:
(其中
)与曲线
,
的交点分别为A,B(A,B异于原点),求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b951b1898079b558ccfb555da9a33d1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7347b88954b4a322f82c38a6af61e5c6.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272940da1f0e6c00113c9095651e0e87.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/d4ab1c19147ff7ccc1050c745ef08b47.png)
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9卷引用:福建省厦门第一中学2018-2019学年高二下学期第二次月考数学(理)试题
2 . 设双曲线
上两动点
离心角分别为
,若
,试求双曲线在
两点处切线的交点轨迹.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60c46676928d20cffd26a8589b5e622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
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3 . 在直角坐标系中,以原点为极点,
轴的正半轴为极轴建立坐标系.已知曲线
,过点
的直线
的参数方程为
(
是参数),直线
与曲线
分别交于
,
两点.
(1)写出直线
的普通方程与曲线
的直角坐标方程;
(2)若
,
,
成等比数列,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee3ed5747742944e9e6d7e3de15da34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38b559f160470e4ae99634b95e2537c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28d702293147b2c08c374b51834e98a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.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)
(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/17a92b933377ae3453fb36a171c521c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac35b1e8a952aac4f4cdaaf02d868d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a62cc2e0f761199eab7bd6c9c102e636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-01-08更新
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2卷引用:宁夏石嘴山市第三中学2016届高考一模数学(文)试题
4 . 以平面直角坐标系的原点为极点,正半轴为极轴,建立极坐标系,两种坐标系中取相同的长度单位,设点A的极坐标为
,直线l过点A且与极轴成角为
,圆C的极坐标方程为
.
(1)写出直线l参数方程,并把圆C的方程化为直角坐标方程;
(2)设直线l与曲线圆C交于B、C两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2137436455816a17f748acd06e7eb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e446bf5189a92b165a80bf32d467572d.png)
(1)写出直线l参数方程,并把圆C的方程化为直角坐标方程;
(2)设直线l与曲线圆C交于B、C两点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843363e1d63e1e4b8a6bde5825ef5a4f.png)
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解题方法
5 . 已知曲线C的极坐标方程是
,以极点为原点,极轴为x轴的正半轴建立平面直角坐标系,直线l的参数方程为
(t为参数).
(1)写出直线l的直角坐标方程与曲线C的普通方程
(2)设曲线C经过伸缩变换
,得到曲线
,设曲线C'上任一点
,求M到的直线l的距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f917a2022014d9c19c29eeac84c74e2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093595b64dcd191bd20b70e65425572d.png)
(1)写出直线l的直角坐标方程与曲线C的普通方程
(2)设曲线C经过伸缩变换
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0048a15fc809cbdc75c85ea2f90f61a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22962a2ad892cb6b14ab039a06e8cdc6.png)
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6 . 在平面直角坐标系xOy中,点
(t为参数),若以原点O为原点,x轴的正半轴为极轴建立极坐标系,曲线l的极坐标方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b522cd610b8af1584c73a3d1eb70e0.png)
(1)求点P的轨迹方程.
(2)求一点P,使它到直线l的距离最小,并求最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fadf758d3120dbf95581c2ce6b0d607c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b522cd610b8af1584c73a3d1eb70e0.png)
(1)求点P的轨迹方程.
(2)求一点P,使它到直线l的距离最小,并求最小值.
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解题方法
7 . 直线l过点
,且倾斜角为
,曲线
(θ为参数).
(1)写出直线l的参数方程的标准形式,并求曲线C的普通方程;
(2)若直线l与曲线C交于A,B两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3b2e58daa2ace0f4071146918d7be5.png)
(1)写出直线l的参数方程的标准形式,并求曲线C的普通方程;
(2)若直线l与曲线C交于A,B两点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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8 . 在直角坐标系
中,曲线
的参数方程为:
(θ为参数),以直角坐标系
的原点O为极点,x轴的正半轴为极轴,取相同的单位长度建立极坐标系,已知直线l:
.
(1)试写出直线l的直角坐标方程和曲线
的普通方程;
(2)在曲线
上求一点P,使点P到直线l的距离最大,并求出此最大值.
![](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/1c3ddf72219574fd5aaee532f2fca694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e818987c4b1a88e0d3721c6861b696be.png)
(1)试写出直线l的直角坐标方程和曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
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2024-01-06更新
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2卷引用:宁夏石嘴山市第三中学2017届高三上学期期末数学(文)试题
名校
9 . 在直角坐标系
中,曲线
的参数方程为
(t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,直线
的极坐标方程
.
(1)求
和
的直角坐标方程;
(2)直线
与C交于MN两点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d898de3e32d7cd0cea11e5e3eb7581.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18baf286c139692f7482b4f72dcf4447.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
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2024-01-05更新
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2卷引用:广东省广州市从化中学2020届高三上学期第三次月考数学(理)试题
解题方法
10 . 已知曲线
的参数方程为
(
为参数),以直角坐标系原点
为极点,
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
,若
与曲线
相交于异于原点的两点
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcdbe7743ca54add864ccc966b09e39.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)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfbff6c5226345e724a699a98a97ca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.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/e2b83beedb3438153e6f728545fe3e03.png)
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