1 . 在平面直角坐标系
中,已知点
,
,记
的轨迹为
.
(1)求
的方程;
(2)过点
的直线
与
交于
两点,
,
,设直线
的斜率分别为
.
(i)若
,求
;
(ii)证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871868260c78a20767eae39bcdb97476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eed5b1b5a80e66f5a6cd08be019376c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a16143ae1edcef852e367f50db8869f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca1726d463bd741c904abd9b6589056.png)
(i)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e607c2f7ae494246768832acb0d54a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3342ecc389773431bc3f64410e41191.png)
您最近一年使用:0次
2024-03-07更新
|
473次组卷
|
4卷引用:江苏省南京市五校2023-2024学年高二下学期期初调研测试数学试题
2 . 在平面直角坐标系
中,已知圆E:
和定点
,P为圆E上的动点,线段
的垂直平分线与直线
交于点Q,设动点Q的轨迹为曲线C.
(1)求曲线C的方程;
(2)若
为曲线
上两点,点
在直线
上,试在①直线
过点
;②
;③直线
过点
三者中选择其中两者作为条件,剩下的一个作为结论,并证明其成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe3492a178084a1b8973e9e17bb165b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d314b47d37c9f58e05ad11f3e68e27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
(1)求曲线C的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f6c870d99382487249cf481f275e28d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe12fb284fc8e2502c9043be594c852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5482b84882a5a4cd2e365e2b98dcb54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e544ce30f9debf4e626677378bbcbff.png)
您最近一年使用:0次
3 . 希腊数学家帕普斯在他的著作《数学汇篇》中,完善了欧几里得关于圆锥曲线的统一定义,并对这一定义进行了证明,他指出,到定点的距离与到定直线的距离的比是常数
的点的轨迹叫做圆锥曲线:当
时,轨迹为椭圆;当
时,轨迹为抛物线;当
时,轨迹为双曲线,则方程
表示的圆锥曲线为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42b7ac29311c13aa538f3f48cb513b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09dbcaa127022fbd6b6f13345196408a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58c44592477e5cab15cd165ff9b3d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd04d1e6c67aa5a825f578f05742a5e2.png)
A.椭圆 | B.双曲线 | C.抛物线 | D.以上都不对 |
您最近一年使用:0次
2024-01-27更新
|
351次组卷
|
2卷引用:江苏省盐城市响水中学2023-2024学年高二上学期期末数学试题
名校
解题方法
4 . 已知点
,动点
满足
.
(1)求点
的轨迹
的方程;
(2)若轨迹
的左右顶点分别为
,直线
与直线
交于点
,直线
与轨迹
交于相异的两点
,当点
不在
轴上时,分别记直线
与
的斜率为
,
,求证:
是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669801de4f9ae277b2d7a6ad5baba12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450c0e0334e63d27be931512d95d2b90.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若轨迹
![](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/b11449658adfc07dcf4fc0b25e7ed7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54ea1c0c4903b3222aad364b52b5f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](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/a2a3f348a942d468f0d77c0dfbb41d87.png)
您最近一年使用:0次
2024-01-25更新
|
1019次组卷
|
2卷引用:江苏省盐城市2023-2024学年高二上学期1月期末联考数学试题
解题方法
5 . 如图,在圆
(
)上任取一点
,过点
作
轴的垂线段
,
为垂足.当点
在圆上运动时,线段
的中点
的轨迹是椭圆,那么这个椭圆的离心率是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3503d330608e7138d1b529aba4512fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/5e38e829-bc1d-486c-9d1b-d58922dc00ab.png?resizew=157)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-01-11更新
|
484次组卷
|
3卷引用:江苏省2023-2024学年高二上学期期末迎考数学试题(B卷)
6 . 在平面直角坐标系
中,点A是圆
上一动点,点B是圆
上一动点,当
三点共线时,过点B作x轴的垂线,垂足为H,过点A作
的垂线,垂足为P.
(1)请判断动点
的轨迹,并求出其轨迹方程;
(2)记(1)中轨迹为曲线C,在曲线C的上半部分取两点M,N,若
,且
.
①当
时,求四边形
的面积;
②求四边形
的面积最大时点M的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f808962ba6a716b7ae74a3b3d20c6a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/609465bd33590642c18323c03f39c23f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef644115c956ed62c3da8310c6f67ecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
(1)请判断动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee82573986d4fa6a7ee1b5f397edae.png)
(2)记(1)中轨迹为曲线C,在曲线C的上半部分取两点M,N,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/598d0e190c5a6c58543e16dd68b14957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe98ef73331666776210e74ea36555f8.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b032d78f28236864b69803022e442b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75bfa01c4013b4710a7fb71c305c0b7.png)
②求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75bfa01c4013b4710a7fb71c305c0b7.png)
您最近一年使用:0次
2024-01-06更新
|
318次组卷
|
3卷引用:江苏省2023-2024学年高二上学期期末迎考数学试题(B卷)
解题方法
7 . 如图,长为a(a是正常数)的线段AB的两个端点A,B分别在互相垂直的两条直线上滑动,点M是线段AB上靠近A的三等分点,则下列说法正确的为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/204491b5-d75e-4568-9c31-c4d0ea0a68e0.png?resizew=155)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/204491b5-d75e-4568-9c31-c4d0ea0a68e0.png?resizew=155)
A.点M的轨迹是圆 | B.点M的轨迹是椭圆且离心率为![]() |
C.点M的轨迹是椭圆且离心率大小与a有关 | D.点M的轨迹不能确定 |
您最近一年使用:0次
8 . 在平面直角坐标系中,
、
、
三点共线,且
,
.当
、
分别在
轴和
轴上运动时,动点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)若过点
且斜率分别为
,
的两条直线与曲线
分别交于点
、
、
、
,并满足
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/fc5488cee89a2911f09137e1cfc3cf58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0588df1f5fa542e811c6aef7960c0acd.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b32a92039ba74fca3ff47ec3b184c41.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ef080e2a4f10b603cfc251f7e5ffa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
您最近一年使用:0次
9 . 已知平面上三点A,B,C.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/a3fe0fe3-41fe-4dda-af92-01098391da67.png?resizew=142)
(1)若该三点构成三角形,且
,建立适当的坐标系,用解析法证明:底边
上任意一点到两腰的距离之和等于一腰上的高;
(2)若
,
,且动点B满足
.
①求动点B的轨迹方程;
②当动点B满足
时,求B点的纵坐标.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/a3fe0fe3-41fe-4dda-af92-01098391da67.png?resizew=142)
(1)若该三点构成三角形,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5a4bf8028cee9396367b68ea8e6f80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95e84f5c91c910aaafc5e74dbfbdf59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e24f172a287592897ea4378a2ad29013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dcb7c773e89873d10a4754ef1d5909d.png)
①求动点B的轨迹方程;
②当动点B满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3493ae59c386883c6a7eab670ee251c7.png)
您最近一年使用:0次
10 . 已知点
,点
分别是直线
,
上的动点,且
,
的中点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)过点
作两条相互垂直的直线
与
,若
与曲线
交于
,
两点,
与曲线
交于
,
两点,求
的取值范围.
![](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/338db305ea04d0af8bd3a1bebf33a21d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd63ae2b424a7584dfbcfc24968d88c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/529b4836786aca156de325464ea2ecd9.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/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71fb572a6f07dcade5332bea766020f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f2813ee8f26cca880b6427f5f545d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f2813ee8f26cca880b6427f5f545d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23da63240b8224a5baaa5c6826ae6917.png)
您最近一年使用:0次