1 . 点
为极坐标系中的一点,给出如下各点的坐标:①
;②
;③
;④
.其中可以作为点
关于极点的对称点的坐标的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adc55b3ddd4eb6a59833882cd7f2f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871534be7754c5aa0e44b3883b0781db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bf791b7ef8491139a6a4d32342c670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b93df54612e3a2e5944e9b7c0776f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186fd5251950f62ccba1402ede4f9145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.①② | B.①③ | C.②③ | D.②④ |
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2 . 参数方程![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc15c2afe4d93fdf31637732fa1aab94.png)
为参数
表示的曲线是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc15c2afe4d93fdf31637732fa1aab94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104c87717fcdb3b4513c4ea57bd03bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
A.直线 | B.圆 | C.椭圆 | D.双曲线 |
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2卷引用:陕西省咸阳市实验中学2021-2022学年高二下学期阶段性检测(一)数学(文)试题
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解题方法
3 . 若点
在曲线
(
为参数)上,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c085e8bb6f9894780bc69dd8b96b734d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf99adccc80f28343fedd8d0aad7429.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 在平面直角坐标系
中,圆
,以原点
为极点,
轴正半轴为极轴建立极坐标系,圆心
在直线
上.
(1)求圆
的极坐标方程;
(2)过
作两条互相垂直的直线
,其中
与圆
交于
两点,
与圆
交于
两点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a58b2a88e160e523bdc0f953ea0ed08.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/ce90d1e663ca4df813f44dbd81da14a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f65c19068583d5a7704f635ee24dc7f.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9cda46e575acf64941ea0964b89ee99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffc62c28c53286cd17e9eb997af7221.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
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5 . 在同一平面直角坐标系中,经过伸缩变换
后,曲线
变为曲线
,则曲线
的方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c158276175f2db250a569ed74ca3d766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46d67063727089919c0a5d02667defc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
6 . 在平面直角坐标系
中,已知直线
与曲线
(
为参数)恰有两个不同的交点,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3348aa4cbf8f53e4ba7247acc94da5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3534b1517ba7a64a8c72ec0ab5ecfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
7 . 在平面直角坐标系中,曲线C的参数方程为
(
为参数),直线
的参数方程为
(t为参数).
(1)写出曲线C与直线
的普通方程;
(2)设点
,点N在曲线C上.以坐标原点O为极点,x轴正半轴为极轴建立极坐标系,求线段
中点P的轨迹的极坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a11e66d3257ff29badb860916f78dc9.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/2e00e4e1da6c68c65bd7f3842277b1c5.png)
(1)写出曲线C与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cf8af6e62058cc4e2d83d5da7f4c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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8 . 在极坐标系中,
是经过点
且倾斜角为
的直线,曲线
的极坐标方程为
.
(1)求
的极坐标方程;
(2)若曲线
的极坐标方程为
,设
与
和
的交点分别为
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cf89e94eb51129f144d9809ec290f7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ab1f834717d760ae99e852beaa5582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.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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9 . 在平面直角坐标系
中,曲线
(
为参数),将曲线
上的所有点的横坐标缩短为原来的
,纵坐标缩短为原来的
后得到曲线
.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)求曲线
的极坐标方程和直线
的直角坐标方程;
(2)设直线
与曲线
交于不同的两点
、
,已知点
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b75e2c7a43dbee85d3256a6ee24e8a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802e162b98c280720fcb909cf392fda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.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/d5bea9f83d8a99eea91d6f99058ba6e7.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/2bcb79087603c47aec81fe61155b5ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9486e4e76ff07c6c47091e0e4b8bcd7d.png)
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10 . 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
和
的极坐标方程分别为
和
和
与曲线
分别相交于
两点(
两点异于坐标原点).
(1)求
的极坐标方程;
(2)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/c2c4e4f93c2211f5a7bdd51760b7b614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a40d2cf43fce0c99dff3470d554eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3f2e3a093c2b85098f01618a8f9661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.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/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
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