1 . 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
的直角坐标方程,并指出其表示何种曲线;
(2)设直线
与曲线
交于
两点,若点
的直角坐标为
,试求当
时
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/b55f55dcc571dbcfd32fd224b276ce67.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/2e0aa98c51f784323ff85f74e018868f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b334e2eaa7e8fb79cef8208b56ee4f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96144368b1b5ca55648a797580f022e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a430c41f782c5c12f68a49c5d0cb1ee2.png)
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名校
2 . 在极坐标系下,点
为曲线
:
在极轴
上方的一点,且
,以极点为原点,极轴为
轴正半轴建立平面直角坐标系
.
(1)求曲线
的参数方程;
(2)以
为直角顶点,
为一条直角边作等腰直角三角形
(
在
的右下方),求点
轨迹的极坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03eeea60522142234171f2705940581b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0cb878349009a779d94b1bc40319bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5880c3a44e340c0689833ec809429670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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2023-05-18更新
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362次组卷
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5卷引用:黑龙江省哈尔滨市第九中学校2022届高三下学期第五次模拟考试(理科)数学试题
黑龙江省哈尔滨市第九中学校2022届高三下学期第五次模拟考试(理科)数学试题(已下线)考向45坐标系与参数方程(重点)-1(已下线)专题10-1 极坐标与参数方程题型归类(讲+练)-1(已下线)专题21 圆锥曲线中的轨迹方程的求法-1四川省绵阳市绵阳中学2023届高三高考模拟理科数学试题(三)
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3 . 在直角坐标系
中,曲线
的参数方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ad7a6ab7b8d8d094fd41ebcc57b551.png)
为参数),
是
上的动点,
点满足
点的轨迹为曲线
.
(1)求
的参数方程;
(2)在以
为极点,
轴的正半轴为极轴的极坐标系中,射线
与
的异于极点的交点为
,与
的异于极点的交点为
,求
.
![](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/68ad7a6ab7b8d8d094fd41ebcc57b551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608172a5a6acb7aec81dc3791c2f287e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/9bf3c11311568b9d6363f458cbd02c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)在以
![](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/0bc1f08c7640e62e8717abf4d44a6c83.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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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2022-09-21更新
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4卷引用:黑龙江省哈尔滨市第三中学校2021-2022学年高三上学期期末数学(文)试题
名校
解题方法
4 . 若
,则
的最大值是____________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5fbef7f8c4a637803773647e17388b5.png)
您最近一年使用:0次
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5 . 在平面直角坐标系
中,曲线
:
,曲线
:
(
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.
(1)求曲线
,
的极坐标方程;
(2)若射线
与曲线
,
的公共点分别为A,B,求
的最大值.
![](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/cbe0890043f34b4575bf7bb3a773e32b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b951b1898079b558ccfb555da9a33d1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f2e72691e34ec4ab7e9ff3a4f9cf78.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/ac0f4498f2ff1e890d75d6d51ba6cbe8.png)
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2022-06-06更新
|
962次组卷
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5卷引用:黑龙江省鸡西市第四中学2022届高三三模数学(理)试题
黑龙江省鸡西市第四中学2022届高三三模数学(理)试题(已下线)2022年全国高考甲卷数学(理)试题变式题13-16(已下线)2022年全国高考甲卷数学(理)试题变式题13-16题(已下线)2022年全国高考甲卷数学(理)试题变式题21-23题宁夏北方民族大学附属中学2023届高三上学期月考(一)数学(理)试题
名校
解题方法
6 . 以直角坐标系的原点O为极点,x轴的非负半轴为极轴由建立极坐标系,曲线C的参数方程为
(t为参数),直线l的极坐标方程为
.
(1)已知点
在曲线C上,求a的值;
(2)设点P为曲线C上一点,求点P到直线l距离的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6911b791d998c8e47af24c36e7437942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1016de804ae504953f7a253094cf2ce.png)
(1)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3f889c27aee15849f5dfae07d252e7.png)
(2)设点P为曲线C上一点,求点P到直线l距离的最小值.
您最近一年使用:0次
2022-05-19更新
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538次组卷
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2卷引用:黑龙江省哈尔滨第九中学校2022届高三下学期第四次模拟考试理科数学试题
名校
7 . 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轴的正半轴为极轴建立极坐标系中,直线
:
.
(1)求曲线
上的点与直线
上的点距离的最小值;
(2)将曲线
向左平移1个单位,向下平移
个单位得到曲线
,再将
经过伸缩变换
后得到曲线
,求曲线
上的点到直线
距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fca8110ebacb2a8214fc9fa6b470da7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629b0d5f423aa7ab2a96b65bbc72fda0.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)将曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc23950308a0dfbe8ee8f717c4d71ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384bef25d6a7f4c661e83498628c1409.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384bef25d6a7f4c661e83498628c1409.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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2022-05-18更新
|
1036次组卷
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2卷引用:黑龙江省哈尔滨市第三中学2022届高三下学期第四次高考模拟考试数学(理)试题
8 . 在平面直角坐标系xOy中,直线l的参数方程为
(其中t为参数),以O为极点,x轴正半轴为极轴建立极坐标系,曲线C的极坐标方程为
.
(1)求直线l的普通方程以及曲线C的直角坐标方程;
(2)求曲线C上的点到直线l的距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e5c5d17b9998825559409bbe4695c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7d68ecabdd18089c7ff19f19dbc83d.png)
(1)求直线l的普通方程以及曲线C的直角坐标方程;
(2)求曲线C上的点到直线l的距离的最大值.
您最近一年使用:0次
2022-05-15更新
|
474次组卷
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3卷引用:黑龙江省齐齐哈尔市2022届高三三模理科数学试题
9 . 在平面直角坐标系xOy中,直线l的参数方程为
(t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,曲线C的极坐标方程为
.
(1)写出直线l的普通方程和曲线C的直角坐标方程:
(2)在平面直角坐标系xOy中,设直线l与曲线C相交于A,B两点,若点
恰为线段AB的一个三等分点,求正数m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0093a17234eee18eaaf33fb6fb02d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a51aeb70c8e4fe84d617002f8ca5b478.png)
(1)写出直线l的普通方程和曲线C的直角坐标方程:
(2)在平面直角坐标系xOy中,设直线l与曲线C相交于A,B两点,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a42451bdbef6c82dbaf8e06f0614794.png)
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2022-05-13更新
|
339次组卷
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8卷引用:黑龙江省佳木斯市第一中学2022届高三第三次模拟数学(文)试题
黑龙江省佳木斯市第一中学2022届高三第三次模拟数学(文)试题黑龙江省佳木斯市第一中学2022届高三第三次模拟数学(理)试题安徽省“皖南八校”2022届高三下学期第三次联考理科数学试题安徽省“皖南八校”2022届高三下学期第三次联考文科数学试题(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)文科数学-2022年高考考前20天终极冲刺攻略(四)(6月3日)安徽省合肥市第七中学2022届高三下学期二模(一)理科数学试题(已下线)专题10-1 极坐标与参数方程题型归类(讲+练)-1
10 . 在直角坐标系
中,曲线
的参数方程为
(
为参数),曲线
,以坐标原点
为极点,
轴的正半轴为极轴建立极坐标系.
(1)求曲线
的普通方程和曲线
的极坐标方程;
(2)若曲线
与曲线
,
分别交于
,
两点,求
.
![](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/b40f954d49b404da11388a3e9fcaf539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdce9813dd373037c81d62535e67be18.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2685d91f8404a4c48dfe990b6cde67e.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
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2022-05-11更新
|
840次组卷
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5卷引用:黑龙江省佳木斯市第一中学2022届高三下学期高考押题卷理科数学试题