1 . 在平面直角坐标系
中,
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.
的极坐标方程为
.
(1)求
的直角坐标方程,并指出其图形的形状;
(2)若曲线
与
有且仅有一个公共点,求参数方程
中的
的正切值.
![](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/e85e4038c162f7d84d4905e5cdc2b597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6b60aec15207d0c144c94f2ec428c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152236216f8d1cb39b261108e8fc8b9e.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/17f93b53777fb4061a39c225d189ac60.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5bfa05232c26797f61d439b6d42ac8.png)
(2)若曲线
![](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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
名校
2 . 在直角坐标系
中,以原点
为极点,以
轴非负半轴为极轴,建立极坐标系,直线
的极坐标方程为
,曲线
的极坐标方程为
.
(1)求曲线
与直线
的直角坐标方程;
(2)设曲线
与直线
交于点
,
两点(点
在
轴上方),若点
,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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bdcfd856a7c15bcb7ecd516ba800d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b34a1e7a48f450d883f9a0197e5c9.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设曲线
![](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)
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0772cd4d77ee0cbaaba2fe69cfdc5ad3.png)
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2021-11-01更新
|
848次组卷
|
3卷引用:黑龙江省哈尔滨市第三中学2021-2022学年高三上学期期中考试数学(文)试题
3 . 在平面直角坐标系
中,已知曲线
的参数方程为
(
参数),直线
的参数方程为
(
为参数).
(1)求直线
与曲线
的普通方程,并说明曲线
是哪一种曲线;
(2)设
,
是直线
与曲线
的公共点,点
的坐标为
,求
的值.
![](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/4f1e4cb5967d67eba9a188452f8829f5.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/21d0929569fe8f4d589c02a1247359a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)求直线
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/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/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa1d29d610bf5f13e812124797f2cb79.png)
您最近一年使用:0次
2021-11-01更新
|
898次组卷
|
2卷引用:四川省成都市蓉城名校联盟2021-2022学年高三上学期第一次联考文科数学试题
4 . 已知曲线
的极坐标方程为
,以极点为原点,极轴为
轴的正半轴建立平面直角坐标系,直线
的参数方程为
(
为参数,
),
.
(1)求曲线
的直角坐标方程,并判断该曲线是什么曲线?
(2)设过点
的直线
与曲线
交于
,
两点,求弦
长度的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a23d39625e9a19f99adcfac54acd86b.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/ca75a96e78f2ebf4d88e4bec5c4c2b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/995ec593baa4ef50b6d87c78380953d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7368e58f66071086476b72ef86e1fa.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2021-10-31更新
|
444次组卷
|
2卷引用:云南省峨山彝族自治县第一中学2022届高三10月测试数学(理)试题
5 . 已知曲线C的参数方程为
(t为参数),直线l过点
,倾斜角为
.
(1)写出曲线C的普通方程和直线l的参数方程;
(2)直线l交曲线C于A,B两点,若
,求直线l的倾斜角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b79f8be02ddd0eea256c7f45978e1bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9fcd21a02ef02808a602b8be0130b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(1)写出曲线C的普通方程和直线l的参数方程;
(2)直线l交曲线C于A,B两点,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a8e83b32c076e09c636225c981cbd7.png)
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2021-10-30更新
|
796次组卷
|
2卷引用:云南省师范大学附属中学2022届高三高考适应性月考卷(四)数学(理)试题
6 . 在平面直角坐标系
中,圆C的参数方程为
(
为参数),直线
经过点P(1,1),倾斜角![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c95fa7f61564978c8e26616bc14449e.png)
(1)写出直线
的参数方程,把圆C的参数方程转化为普通方程;
(2)设
与圆C相交与两点A,B,求点P到A,B两点的距离之积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ef09d524897bd8ea496d82bd24820e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c95fa7f61564978c8e26616bc14449e.png)
(1)写出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
7 . 在平面直角坐标系xOy中,曲线
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
的极坐标方程为
.
(1)求曲线
的普通方程和曲线
的直角坐标方程:
(2)已知
,曲线
与曲线
相交于A,B两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c09022cc057ed9b0c22159accc0dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3bbadbbd68081a3ee8263623bb613da.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
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.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/559d66fd8b309fd440ce9bda78a579c9.png)
您最近一年使用:0次
2021-10-26更新
|
872次组卷
|
6卷引用:吉林省双辽一中长岭三中等重点高中2021-2022学年高三上学期10月联考数学(文)试题
8 . 在平面直角坐标系
中,P为曲线
(
为参数)上的动点,将P点的横坐标不变,纵坐标变为原来的一半从而得到动点Q,记动点Q的轨迹为
.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)设点M的直角坐标为
,A,B是曲线
上的两个动点,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d683a098b8b702334da9e2fab2d0cb04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)设点M的直角坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6554ac3dff4a59833e407db887f6e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b68262dfb35e058124edbe859fa186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb786fd53d142b7d8b3e08352b0aae2d.png)
您最近一年使用:0次
2021-10-25更新
|
945次组卷
|
2卷引用:贵州省贵阳市第一中学2022届高三10月高考适应性月考数学(文)试题(二)
名校
9 . 在平面直角坐标系
中,曲线
的参数方程为
(
),在以坐标原点为极点,
轴的正半轴为极轴的极坐标系中,直线
的方程为
.
(1)求曲线
的普通方程和直线
的直角坐标方程;
(2)已知点
,直线
与曲线
相交
,
两点,点
是弦
的中点,求三角形
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/ff3b443181e85187095a39de9512e4c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417a7baca0753ba9ad45fe148d5d291c.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/649361e842399b796c4cb0b1fe75e2d9.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0af1a9647a129a692715564967a8ef6.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dd71a8cbe8d1da754b8b4ed18bb0048.png)
您最近一年使用:0次
2021-10-23更新
|
774次组卷
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3卷引用:四川省南充市2022届高考适应性考试(零诊)理科数学试题
10 . 在直角坐标系
中,已知点
和直线
(
为参数,
);以
为极点,
轴正半轴为极轴建立极坐标系,圆
的极坐标方程为
.设直线
与圆
的交点为
,
.
(1)写出圆
的直角坐标方程,并求当点
为线段
的中点时直线
的普通方程;
(2)当
变化时,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c9708ef0dc6d6f5dcf6596d3e4f6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d1798536ea6e23554c34b438fef1dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.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/1a0e6059919e8ea5fcb00520cfb229b6.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)写出圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2021-10-23更新
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554次组卷
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4卷引用:四川省巴中市2021-2022学年高三上学期“零诊”数学(文科)试题