1 . 在平面直角坐标系xOy中,已知曲线C的参数方程为
(t为参数).以O为极点,x轴正半轴为极轴建立极坐标系,直线l的极坐标方程为
,其中α为倾斜角,且
.
(1)求曲线C的普通方程和直线l的直角坐标方程;
(2)设l与曲线C相交于P,Q两点,直线OP,OQ的斜率为
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d9cbe04956ef4b95ef024abd8996a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96f0838287a18587c531ee73b4dd71ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dac81d455c635326354f30f129e0b00.png)
(1)求曲线C的普通方程和直线l的直角坐标方程;
(2)设l与曲线C相交于P,Q两点,直线OP,OQ的斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
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名校
解题方法
2 . 在直角坐标系
中,
,以坐标原点为极点,
轴的非负半轴为极轴建立极坐标系,已知圆锥曲线
的极坐标方程为
,
、
为
的左、右焦点,过点
的直线
与曲线
相交于A,
两点.
(1)当
时,求
的参数方程;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e7f4a57688b0613a901a8f9e32e46b.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/5b41b0a52703647298bb8209ae393ade.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36bce273e1a2f40613e1160e5a9a353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13c2ef75d26088d0959eb993868ef798.png)
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3 . 在直角坐标系xOy中,已知直线l的方程为
,曲线C的参数方程为
(α为参数).以O为极点,x轴的正半轴为极轴建立极坐标系.
(1)求直线l的极坐标方程和曲线C的普通方程;
(2)设直线
与曲线C相交于点A,B,与直线l相交于点C,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/896aa4ffc1f71505384513f8fed8591d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ce418a8d149d03c766281e2415eb43.png)
(1)求直线l的极坐标方程和曲线C的普通方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082990da1f11a1a7be4fc3935c0d526e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f353bf37e83b723b3b74821feb91db.png)
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5卷引用:江西省九江市2023届高三高考二模数学(文)试题
江西省九江市2023届高三高考二模数学(文)试题江西省九江市2023届高三高考二模数学(理)试题(已下线)专题20坐标系与参数方程(已下线)专题20坐标系与参数方程.(已下线)专题10-1 极坐标与参数方程题型归类(讲+练)-2
名校
4 . 在平面直角坐标系xOy中,曲线C的参数方程为
(
是参数),直线l的普通方程为
,以坐标原点为极点,x轴的正半轴为极轴建立极坐标系.
(1)求曲线C的普通方程和直线l的极坐标方程;
(2)若P是曲线C上任意一点,求点P到直线l的距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5e109e021b199157e70a2a8b01f3cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19556a290cd4e98e84b584d30f466614.png)
(1)求曲线C的普通方程和直线l的极坐标方程;
(2)若P是曲线C上任意一点,求点P到直线l的距离的取值范围.
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解题方法
5 . 在直角坐标系
中,已知曲线
的参数方程为
(
为参数),以
为极点,
轴的正半轴为极轴建立极坐标系,直线
的极坐标方程为
(
为直线
的倾斜角).
(1)求直线
的直角坐标方程和曲线
的普通方程;
(2)设
,直线
与曲线
相交于
两点,求
的最大值.
![](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/40814c3d991b0068b9279b5504651544.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ac52967afa15d89f919a8a03998a4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e951187d5c8005fc8ab8efa1342c8be.png)
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9卷引用:江西省九江市2023届高三一模数学(理)试题
6 . 在平面直角坐标系xOy中,以原点O为极点,x轴的非负半轴为极轴建立极坐标系,两点P,Q的极坐标分别为
,以OQ为直径的圆记为⊙C.
(1)求⊙C的直角坐标方程;
(2)若直线l经过点P与⊙C相交于A,B两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e36cd93deaad4b58f77a194704470ee.png)
(1)求⊙C的直角坐标方程;
(2)若直线l经过点P与⊙C相交于A,B两点,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0f1f2f39960424e23b19dcbb0c184a.png)
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名校
7 . 在平面直角坐标系xOy中,曲线C的参数方程为
(
为参数),以原点O为极点,x轴的非负半轴为极轴建立极坐标系,直线l的极坐标方程为
.
(1)求曲线C的普通方程和直线l的直角坐标方程;
(2)设点M的极坐标为
,直线l与曲线C交于A,B两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9380dca2fd7fb8d20c0f5af481d613c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/649361e842399b796c4cb0b1fe75e2d9.png)
(1)求曲线C的普通方程和直线l的直角坐标方程;
(2)设点M的极坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c22b1e5f86598a830d503d0746f81d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bba91242bb7841a41711f02db45fdc0.png)
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名校
8 . 在平面直角坐标系
中,以
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
,曲线
的极坐标方程为
.
(1)求曲线
的直角坐标方程;
(2)若曲线
上恰有三个点到曲线
的距离为
,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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95173799039693fd11ac80bb0ed54b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a78c94fe991381a0a3770001774df5c.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.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/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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9 . 在直角坐标系
中,曲线
的参数方程为
(
为参数).已知M是曲线
上的动点,将OM绕点O逆时针旋转
得到ON,设点N的轨迹为曲线
.以坐标原点为极点,x轴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
,
分别相交于异于极点O的A,B两点,求
的值.
![](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/64f23bb05e586ec0a3d42bdf95399ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ff7caec4fdd8fb54a3ffbff9692414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.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/b38b7ab47112d704df2ace62160aec3e.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/3f4dfec890cdfdda355e19463f3be813.png)
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10 . 在平面直角坐标系xOy中,已知直线l的普通方程为
,曲线E的参数方程为
(
为参数).
(1)以原点O为极点,x轴正半轴为极轴建立极坐标系,求直线l及曲线E的极坐标方程;
(2)若P为曲线E在第一象限上一点,射线OP按逆时针方向旋转
,与直线l相交于点Q,若
的面积为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/844b0ce7dd3693fa9ffefaafc8858809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b951b1898079b558ccfb555da9a33d1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(1)以原点O为极点,x轴正半轴为极轴建立极坐标系,求直线l及曲线E的极坐标方程;
(2)若P为曲线E在第一象限上一点,射线OP按逆时针方向旋转
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802e162b98c280720fcb909cf392fda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ae743852e53bb3a32144cfa423d2bf0.png)
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