名校
1 . 平面直角坐标系xOy中,已知椭圆C:
的离心率为
,且点
在椭圆C上.椭圆C的左顶点为A.
(1)求椭圆C的方程
(2)椭圆的右焦点且斜率为
的直线与椭圆交于P,Q两点,求三角形APQ的面积;
(3)过点A作直线与椭圆C交于另一点B.若直线
交
轴于点C,且
,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed6b9540857e386651e191a0a5b5a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d695d4b8eb4f37c2c1bf46a190d461a4.png)
(1)求椭圆C的方程
(2)椭圆的右焦点且斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(3)过点A作直线与椭圆C交于另一点B.若直线
![](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/83ff26eeabfaef6e944082999e39e814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2020-04-06更新
|
504次组卷
|
3卷引用:江苏省苏州市吴江区2019-2020学年高三上学期第二次月考数学试题
名校
解题方法
2 . 已知椭圆
的左右焦点分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84d316b10430afac5b0c065f31e1b2c.png)
,上顶点为B,离心率为e,点P在椭圆上(异于点B).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/b021f21c-8786-4848-8971-fc37ef43da6a.png?resizew=162)
(1)若椭圆C经过点
及
,求
的取值范围;
(2)记直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c12279880baa3b90297797bf4d29a265.png)
的斜率分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c87cef1d0bd8b2ee3476a5fa4dbbdc7.png)
,若
,且
,求椭圆C的离心率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84d316b10430afac5b0c065f31e1b2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/b021f21c-8786-4848-8971-fc37ef43da6a.png?resizew=162)
(1)若椭圆C经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c3988d58a90ce85be4e65c4a86de45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12604a5a6371ddb77722d04006f5d5eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b51ba4eb57c3dad6a9356d4b70dc384.png)
(2)记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c12279880baa3b90297797bf4d29a265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83e02c09428538ce8ae136cff26d3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c87cef1d0bd8b2ee3476a5fa4dbbdc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf1ac7607f9d0a1639ec59757aca5d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad7dcfc3e70b0b4c3c93136252b9037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db821941a51ba432ffad4ba5cb253cfc.png)
您最近一年使用:0次
3 . 在平面直角坐标系
中,已知椭圆
的离心率为
,且椭圆
短轴的一个顶点到左焦点
的距离等于
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/7b121abd-0a84-4905-aed8-dd148b0b6048.png?resizew=235)
(1)求椭圆
的方程;
(2)设经过点
的直线
交椭圆
于
两点,弦
的中垂线
交
轴于点
.
①求实数
的取值范围;
②若
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/7b121abd-0a84-4905-aed8-dd148b0b6048.png?resizew=235)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacfc149ede71417fa599c21b5a84cb8.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/c2da6ef88591589f330304297d3abfcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f4ea4bc4c655fd337f8bdd18c493b5.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12c7613bc5c3fc3d8d20b8652fedc736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
名校
解题方法
4 . 在平面直角坐标系
中,椭圆
:
(
)的离心率为
,焦点到相应准线的距离为
,动直线l与椭圆交于
两点.
(1)求椭圆
的标准方程;
(2)若
,求
面积的取值范围.
![](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/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd2981bf2261343f905ec1b5355a3c4.png)
您最近一年使用:0次
2020-03-26更新
|
711次组卷
|
2卷引用:2019届江苏省无锡市第一中学高三下学期2月期初考试数学试题
5 . 平面直角坐标系
中,椭圆C:
(
)左,右焦点分别为
,
,且椭圆的长轴长为
,右准线方程为
.
(1)求椭圆C的方程;
(2)设直线l过椭圆C的右焦点
,且与椭圆相交与A,B(与左右顶点不重合)
(i)椭圆的右顶点为M,设
的斜率为
,
的斜率为
,求
的值;
(ii)若椭圆上存在一点D满足
,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e82fe25db889399bb3ca4ffd5dd5db84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff1e33966ff01e4a394b42a3c65a400.png)
(1)求椭圆C的方程;
(2)设直线l过椭圆C的右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
(i)椭圆的右顶点为M,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2562424a83aae7e4b3f8adf90307961a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b58edb637c5dfa03794f3952de9d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2bb6eabffd165f9580e9dcaaace3a89.png)
(ii)若椭圆上存在一点D满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2738e9e0593d33af7d7177c50e0036a.png)
您最近一年使用:0次
名校
解题方法
6 . 设椭圆
的左右焦点分别为
,
,焦距为
,点
在椭圆的内部,点P是椭圆上的动点,且
恒成立,则椭圆的离心率的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e82fe25db889399bb3ca4ffd5dd5db84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/501daf0a108d8d7a7a36cf54dedf200a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a75d36d6aea9e5d37ff8001a368e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e82018b4636ee48dfc7921a590017a5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
7 . 已知椭圆E:
(
)的离心率是
,
,
分别为椭圆E的左右顶点,B为上顶点,
的面积为2.直线l过点
且与椭圆E交于P,Q两点(P,Q异于
,
)
(1)求椭圆E的标准方程;
(2)求
的面积最大值;
(3)设直线
与直线
的斜率分别为
,
,求证:
为常数,并求出这个常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737029b90a384c2b48973b84bfe74b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d776a89f4fd29dccffe1040069d59ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
(1)求椭圆E的标准方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45b8b000c9c286bff8a480dbf03b513.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e935bb9d7b7115429edbd1e7469af65.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/67351fe10fcfc3f9072eec4c60bfaaa5.png)
您最近一年使用:0次
2020-03-25更新
|
311次组卷
|
2卷引用:江苏省南通市海门中学2019-2020学年高二上学期期中数学试题
解题方法
8 . 如图,在平面直角坐标系
中,已知椭圆
的离心率为
且右焦点
到右准线
的距离为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/70259ee7-4ec3-4123-a11c-872e850294ec.png?resizew=159)
(1)求椭圆
的标准方程:
(2)过点
的直线与椭圆
交于
两点,与
交于点
是弦
的中点,直线
与
交于点
.若
与
的面积之比是
,求
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/70259ee7-4ec3-4123-a11c-872e850294ec.png?resizew=159)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0664a68104a5370205d9d0a80d8862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](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/4c6025da1f98c4e9aa6454dc535dd426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985b383be47791e0409e542225982299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca8b26c3ad6d892590290a2304126bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
9 . 如图所示,在平面直角坐标系
中,点
是抛物线
上的点,直线
交直线
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/b939912a-70c3-4105-b6b7-8f31407db036.png?resizew=155)
(1)求
长度的最小值;
(2)若点
也是抛物线
上的点,且
,直线
交直线
于点
.求四边形
的面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f4123c19136d3a4dc040dce8e34e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd24f3c4bc9f9a75d4b28630bb630d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/b939912a-70c3-4105-b6b7-8f31407db036.png?resizew=155)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f4123c19136d3a4dc040dce8e34e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8dcca60ba6144abbf47abd51d1f63f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd24f3c4bc9f9a75d4b28630bb630d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2019·江苏南通·一模
名校
10 . 在平面直角坐标系
中,已知定点
,点
在
轴上运动,点
在
轴上运动,点
为坐标平面内的动点,且满足
,
.
(1)求动点
的轨迹
的方程;
(2)过曲线
第一象限上一点
(其中
)作切线交直线
于点
,连结
并延长交直线
于点
,求当
面积取最小值时切点
的横坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e48f79069ada435c8225a124f149c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa3da6f509c1fd6041f2fa0d00a29ce.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b79ca81f286d8aeed52f91ee13ce0d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75f702bfe1a376398286f1dc3daf8c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75af77f184b8d76a881874298852081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56844fb3f989204b45c68d8751a1e6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
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2020-02-23更新
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4卷引用:【市级联考】江苏省如皋市2019届高三教学质量调研(三)数学试题
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