名校
1 . 直角坐标系
中,曲线
的方程为
.以坐标原点
为极点,
轴的正半轴为极轴建立极坐标系,点
,曲线
的极坐标方程为
.
(1)求
的极坐标方程与
的直角坐标方程;
(2)设直线
过点
交
于点
(异于原点),射线
,
分别交
于点
,
,求证:
为定值.
![](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/44d12ebd10f6c0bcf98be52c32b107f1.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/894f3d2b4ff914de6970332d3f7efd8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60db761ca3a4f55f13d470409375a9a3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.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/acb8956ebcde7cf0f1011a2fc1888e15.png)
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2 . 在平面直角坐标系
中,直线
的参数方程为
(
为参数,
为
的倾斜角),以原点
为极点,
轴正半轴为极轴,建立极坐标系,曲线
的极坐标方程为
,直线
,
,
,与曲线
分别交于不同于极点
的三点
,
,
.
(Ⅰ)若
,求证:
;
(Ⅱ)当
时,直线
过
、
两点,求
与
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/65badaead3c9b3659685982d45317d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cf89e94eb51129f144d9809ec290f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c54258755a1798a586a77765e2b0066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d814b21a6f035295fd44469de410575f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96812028b6da3d9d5c92d2055d4cab01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2d18b04aed00c2efb0553c6b27699c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dafedbb0f6a649574ab365ada5cb3595.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b211a34415f026d5966c7c7a0eab28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
名校
3 . 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,取相同长度单位建立极坐标系,直线
的极坐标方程为
.
(Ⅰ)求曲线
和直线
的直角坐标方程;
(Ⅱ)直线
与
轴交点为
,经过点
的直线与曲线
交于
,
两点,证明:
为定值.
![](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/6ab29a77dc3d60df0ced82c133d89dd9.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ef8f1ab8f03bbe5005efc2cb0f214a.png)
(Ⅰ)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(Ⅱ)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/559d66fd8b309fd440ce9bda78a579c9.png)
您最近一年使用:0次
2019-06-18更新
|
2932次组卷
|
12卷引用:2020届福建省仙游第一中学高三上学期月考数学(理)试题
2020届福建省仙游第一中学高三上学期月考数学(理)试题福建省泰宁第一中学2020届高三上学期第一阶段考试数学(理)试题【市级联考】河南省八市重点高中联盟“领军考试”2019届高三压轴数学(文)试题【校级联考】河南省八市重点高中联盟“领军考试”2019届高三压轴数学(理科)试题2019年10月广东省广州市天河区高考数学一模(文)试题2019年10月广东省广州市天河区高考数学一模(理)试题2020届辽宁省沈阳市东北育才学校高中部高三第六次模拟数学(文)试题(已下线)专题42 坐标系与参数方程-冲刺2020高考跳出题海之高三数学模拟试题精中选萃甘肃省天水市第一中学2021届高三十模数学(理)试题甘肃省天水市第一中学2021届高三十模数学(文)试题黑龙江省牡丹江市第三高级中学2021-2022学年高三上学期第四次月考数学(文)试题沪教版(2020) 选修第一册 单元训练 第2章 曲线与方程(A卷)
名校
4 . 已知曲线
的极坐标方程为
,倾斜角为
的直线
过点
.
(1)求曲线
的直角坐标方程和直线
的参数方程;
(2)设
是过点
且关于直线
对称的两条直线,
与
交于
两点,
与
交于
两点.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b01da27c299e595731d6d57cf4ace0.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/5946cdc295468832011cb95bf233c7f5.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c29a7e8eea08197bf53164a560bee58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8bc5614c9fb23adc6482b7a728817da.png)
您最近一年使用:0次
2019-03-20更新
|
622次组卷
|
7卷引用:2020届福建省福州第一中学高三上学期期末考试数学(理)试题
5 . 在平面直角坐标系
中,直线
的参数方程为
(
为参数,
为
的倾斜角),以原点
为极点,
轴正半轴为极轴,建立极坐标系,曲线
的极坐标方程为
,三条直线
,
,
与曲线
分别交于不同于极点的三点
,
,
.
(1)求证:
;
(2)直线
过
,
两点,求
与
的值.
![](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/37befaec6ba81de784a13eec3173d30b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7f61f8aff4f209ab171072ccec7746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46418b9fd1116beb8e3ab3cac7c99234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa793287708b46c77bca87fb14c6e0b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d195583dc13b2ed73a1e3d0d6451720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55fe25b4fd31fb3b5f32878aebaecec.png)
(2)直线
![](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/caad7f8af78d4e98554576e8481d042f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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