1 . 在平面直角坐标系
中,曲线
的参数方程为
,(其中
是参数,
).以坐标原点为极点,
轴正半轴为极轴,建立极坐标系,曲线
的极坐标方程为
.
(1)证明:曲线
过定点;
(2)若曲线
与曲线
无公共点,求
的取值范围.
![](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/b917e74c4c06f5efd7de75559b697f12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb82d86ba75f1ec6304521f2b1353f4.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/07ca22561ce6b9d1e217d13d66af3f99.png)
(1)证明:曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
您最近一年使用:0次
2022-04-01更新
|
891次组卷
|
7卷引用:安徽省合肥市肥东县第二中学2021届高三下学期4月月考理科数学试题
名校
2 . 在平面直角坐标系
中.直线
(t为参数,
为l的倾斜角.
)以坐标原点O为极点,x轴的正半轴为极轴建立极坐标系,圆
,直线l与圆C交于M.N两点.
(1)若直线l的斜率
,求弦MN的中点Q的直角坐标与弦长
的值;
(2)若点
.证明:对任意
,有
为定值.并求出这个定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d93809af9f575753664939d93d3515e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6b60aec15207d0c144c94f2ec428c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a8f06e3cb3d28fba293a21e7c4411e6.png)
(1)若直线l的斜率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e69866076dcff686a05e9e91e61e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04eab53049ad5fa477be1958e5141629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79188647c574441c2414c3781a0ef543.png)
您最近一年使用:0次
2022-04-09更新
|
432次组卷
|
2卷引用:安徽省合肥一六八中学2022届高三下学期5月最后一卷文科数学试题
名校
3 . 设
为坐标原点,椭圆
:
经过升缩变换
后变为曲线
,
是曲线
上的点.
(1)求曲线
的方程.
(2)设点
在直线
上,且
.证明:过点
且垂直于
的直线
过
的左焦点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfa06467d100acf800b4d5fbe72d08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba53065eb180a682305fddb95d14b62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d7896d03df0abed59cc696526e1ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.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/a0ed1ec316bc54c37c4286c208f55667.png)
您最近一年使用:0次
名校
4 . 在平面直角坐标系
中,曲线
的参数方程为
(
为参数,
),以
为极点,
轴的正半轴为极轴的极坐标系中,直线
:
与曲线
的交点为
,
,直线
:
与曲线
的交点为
,
.
(1)求曲线
的普通方程;
(2)证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de2963bf266ea8c86a47b4d77fc2183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdbf97b29f90d1a5c001b98f90b0071.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/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e5da28609b29593cedb630a26766b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3004bbf4252dacc929ffe39cb2090fb2.png)
您最近一年使用:0次
2021-05-10更新
|
486次组卷
|
2卷引用:安徽省芜湖市2021届高三下学期5月教育教学质量监控理科数学试题
名校
5 . 在平面直角坐标系
中,曲线
的参数方程为
(
为参数,
),以
为极点,
轴的正半轴为极轴的极坐标系中,直线
(
,
,且
)与曲线
的交点为
,
,直线
与曲线
的交点为
,
.
(1)求曲线
的普通方程;
(2)证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a0dc2369e8529d4e93b311661be7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.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/5fdf31dbe898fc31460d21821a6afd85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d2e40c1f1ff5e667d044767de627fff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eeae4e4940d654f083f1073ba872504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e222c14e46e2fcbb8285eeb18e5ba7.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/707cdc8190586dfa78824ba0a118f553.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3004bbf4252dacc929ffe39cb2090fb2.png)
您最近一年使用:0次
2021-05-14更新
|
807次组卷
|
2卷引用:安徽省芜湖市2021届高三下学期5月教育教学质量监控文科数学试题
6 . 在平面直角坐标系中,曲线C的参数方程为
,(
为参数),直线l的参数方程为
(t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,已知点
(![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e85c633ed1c5d6063f150454ee6b1c.png)
)是曲线C上任意一点.
(I)求证:
;
(Ⅱ)若
,直线
与曲线C相交于不同的两点M,N,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5e1a55579ca43d6fb75a93ad2237d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39894a22c1ef467bc1163c01834dfaad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4775075f1d4847a7401e872eecc43779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e85c633ed1c5d6063f150454ee6b1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fab108d3b154aa152ca5d68be4673a7.png)
(I)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d6bb8c58829535ce10814669bb513c.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a2b8b43e1fe82fc439d145e91b860c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff207928e978a610136a012d20be650.png)
您最近一年使用:0次
7 . 在直角坐标系
,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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b41bf46a462c6cf0a4ba39d748d378.png)
(1)求曲线
的普通方程和直线
的直角坐标方程;
(2)设直线
与
轴的交点为
,经过点
的动直线
与曲线
交于
,
两点,证明:
为定值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e0a4d02005ed2c048b59856ad98c030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4bbec859c7e8286e2f3c2d3b698ef6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.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/e2b41bf46a462c6cf0a4ba39d748d378.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/294f5ba74cdf695fc9a8a8e52f421328.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
2020-05-25更新
|
339次组卷
|
3卷引用:2020届安徽省淮北市高三下学期第二次模拟理科数学试题
名校
8 . 在直角坐标系
中,已知曲线
:
,将曲线
经过伸缩变换
得到曲线
;以直角坐标系原点为极点,
轴的正半轴为极轴建立极坐标系.
(1)写出曲线
的极坐标方程;
(2)若
,
分别是曲线
上的两点,且
,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/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157add92bfbc75a208d95ea10a35cf5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若
![](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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dcb4841ae7bb1d5f91837094cdfcf2c.png)
您最近一年使用:0次
2020-04-06更新
|
400次组卷
|
2卷引用:安徽省六安市舒城中学2019-2020学年高二下学期期末文科数学试题
9 . 在极坐标系
中,曲线
的极坐标方程为
,直线
的极坐标方程为
,设
与
交于
两点,
中点为
,
的垂直平分线交
于
.以
为坐标原点,极轴为
轴的正半轴建立直角坐标系
.
(1)求
的直角坐标方程与点
的直角坐标;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42137d6ea5076b1385940d3450b8d087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72339e813823a31e3436cf7290af5881.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/f52a58fbaf4fea03567e88a9f0f6e37e.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.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/7ee31829d0d4d5f779a957d7df8058ab.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87482d4cc8571f6836c3638d6aeb9fed.png)
您最近一年使用:0次
2020-08-16更新
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420次组卷
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15卷引用:安徽省怀远一中、蒙城一中、淮南一中、颍上一中、涡阳一中2020届高三5月五校联考数学理科试题
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名校
10 . 数学中有许多形状优美,寓意美好的曲线,曲线
就是其中之一(如图).
![](https://img.xkw.com/dksih/QBM/2020/8/11/2525783041941504/2527117615276032/STEM/a89d9799630b40cdb38b31661568666f.png?resizew=128)
(1)以O为极点,x轴的正半轴为极轴建立极坐标系,求曲线C的极坐标方程;
(2)求证:曲线C上任意一点到原点的距离都不超过4.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/616c14c6c7f8e58d7e5d9a528f812894.png)
![](https://img.xkw.com/dksih/QBM/2020/8/11/2525783041941504/2527117615276032/STEM/a89d9799630b40cdb38b31661568666f.png?resizew=128)
(1)以O为极点,x轴的正半轴为极轴建立极坐标系,求曲线C的极坐标方程;
(2)求证:曲线C上任意一点到原点的距离都不超过4.
您最近一年使用:0次
2020-08-13更新
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477次组卷
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4卷引用:安徽省“皖江名校”2020届高三下学期决战高考最后一卷理科数学试题